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Journal articles on the topic 'Local stationary'

Author: Grafiati

Published: 7 February 2023

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1

Conni, Michele, and Hilda Deborah. "Texture Stationarity Evaluation with Local Wavelet Spectrum." London Imaging Meeting 2020, no. 1 (September 29, 2020): 24–27. http://dx.doi.org/10.2352/issn.2694-118x.2020.lim-20.

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In texture analysis, stationarity is a fundamental property. There are various ways to evaluate if a texture image is stationary or not. One of the most recent and effective of these is a standard test based on non-decimated stationary wavelet transform. This method permits to evaluate how stationary is an image depending on the scale considered. We propose to use this feature to characterize an image and we discuss the implication of such approach.

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2

Genton, Marc G., and Olivier Perrin. "On a time deformation reducing nonstationary stochastic processes to local stationarity." Journal of Applied Probability 41, no. 1 (March 2004): 236–49. http://dx.doi.org/10.1239/jap/1077134681.

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A stochastic process is locally stationary if its covariance function can be expressed as the product of a positive function multiplied by a stationary covariance. In this paper, we characterize nonstationary stochastic processes that can be reduced to local stationarity via a bijective deformation of the time index, and we give the form of this deformation under smoothness assumptions. This is an extension of the notion of stationary reducibility. We present several examples of nonstationary covariances that can be reduced to local stationarity. We also investigate the particular situation of exponentially convex reducibility, which can always be achieved for a certain class of separable nonstationary covariances.

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Genton, Marc G., and Olivier Perrin. "On a time deformation reducing nonstationary stochastic processes to local stationarity." Journal of Applied Probability 41, no. 01 (March 2004): 236–49. http://dx.doi.org/10.1017/s0021900200014170.

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A stochastic process is locally stationary if its covariance function can be expressed as the product of a positive function multiplied by a stationary covariance. In this paper, we characterize nonstationary stochastic processes that can be reduced to local stationarity via a bijective deformation of the time index, and we give the form of this deformation under smoothness assumptions. This is an extension of the notion of stationary reducibility. We present several examples of nonstationary covariances that can be reduced to local stationarity. We also investigate the particular situation of exponentially convex reducibility, which can always be achieved for a certain class of separable nonstationary covariances.

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4

Moltchanov, D. "Modeling local stationary behavior of Internet traffic." Journal of Communications Software and Systems 4, no. 1 (March 20, 2008): 41. http://dx.doi.org/10.24138/jcomss.v4i1.236.

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Non-stationary behavior of aggregated IP traffic patterns was demonstrated in a number of studies. However, noneof those did either consider practical aspects of this phenomenon or propose suitable model to capture it. Searching for model for IP traffic aggregates we introduce the concept of local stationarity and demonstrate that it allows to model traffic patterns measured in high-speed operational networks. The proposed model is on-line in nature and suitable for real-time estimation of the traffic state in terms of piecewise covariance stationary stochasticprocess. As a basic tool of the model we use change-pointstatistical test allowing us to dynamically and automaticallydetermine whether statistical characteristics of the traffic pattern changes and, if so, estimate new parameters of the traffic pattern. We provide numerical examples and discuss applications of the proposed model that include but not limited to dynamic resource reservation, routing with guaranteed bandwidth, etc.

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5

Pitman, Jim. "Cyclically stationary Brownian local time processes." Probability Theory and Related Fields 106, no. 3 (November 4, 1996): 299–329. http://dx.doi.org/10.1007/s004400050066.

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6

Deléamont, P. Y., and D. La Vecchia. "Semiparametric segment M-estimation for locally stationary diffusions." Biometrika 106, no. 4 (September 16, 2019): 941–56. http://dx.doi.org/10.1093/biomet/asz042.

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Summary We develop and implement a novel M-estimation method for locally stationary diffusions observed at discrete time-points. We give sufficient conditions for the local stationarity of general time-inhomogeneous diffusions. Then we focus on locally stationary diffusions with time-varying parameters, for which we define our M-estimators and derive their limit theory.

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7

Divine, D. V., J. Polzehl, and F. Godtliebsen. "A propagation-separation approach to estimate the autocorrelation in a time-series." Nonlinear Processes in Geophysics 15, no. 4 (July 23, 2008): 591–99. http://dx.doi.org/10.5194/npg-15-591-2008.

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Abstract. The paper presents an approach to estimate parameters of a local stationary AR(1) time series model by maximization of a local likelihood function. The method is based on a propagation-separation procedure that leads to data dependent weights defining the local model. Using free propagation of weights under homogeneity, the method is capable of separating the time series into intervals of approximate local stationarity. Parameters in different regions will be significantly different. Therefore the method also serves as a test for a stationary AR(1) model. The performance of the method is illustrated by applications to both synthetic data and real time-series of reconstructed NAO and ENSO indices and GRIP stable isotopes.

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8

Cunderlik, Juraj M., Véronique Jourdain, Taha B. M. J. Quarda, and Bernard Bobée. "Local Non-Stationary Flood-Duration-Frequency Modelling." Canadian Water Resources Journal 32, no. 1 (January 2007): 43–58. http://dx.doi.org/10.4296/cwrj3201043.

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9

Feng, Qi, and Thomas Jech. "Local Clubs, Reflection, and Preserving Stationary Sets." Proceedings of the London Mathematical Society s3-58, no. 2 (March 1989): 237–57. http://dx.doi.org/10.1112/plms/s3-58.2.237.

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10

Connaughton, Colm, Alan C. Newell, and Yves Pomeau. "Non-stationary spectra of local wave turbulence." Physica D: Nonlinear Phenomena 184, no. 1-4 (October 2003): 64–85. http://dx.doi.org/10.1016/s0167-2789(03)00213-6.

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11

Robinson, P. M. "Multiple local whittle estimation in stationary systems." Annals of Statistics 36, no. 5 (October 2008): 2508–30. http://dx.doi.org/10.1214/07-aos545.

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12

Tan, Yi, Jesper Ødum Nielsen, and Gert Frølund Pedersen. "Spatial Stationarity of Ultrawideband and Millimeter Wave Radio Channels." International Journal of Antennas and Propagation 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/3212864.

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For radio channels with broad bandwidth resource, such as those often used for ultrawideband (UWB) and millimeter wave (mmwave) systems, the Wide-Sense Stationary Uncorrelated Scattering (WSSUS) and spatial stationary assumptions are more critical than typical cellular channels with very limited bandwidth resource. This paper studies spatial stationarity and bandwidth dependency of the Multipath Component (MPC) parameters, and the concept of local region of stationarity (LRS) is used as the measure of the physical stationarity region. LRS calculation results based on channel measurements show that the size of LRS is bandwidth dependent in all measured bands, 2–4 GHz, 14–16 GHz, and 28–30 GHz. The results in this paper point out that an inappropriate choice of bandwidth in channel parameter estimation could violate spatial stationary assumptions. The paper indicates LRS sizes for different bandwidths in the three bands.

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13

Arrieta-Pastrana, Alfonso, Manuel Saba, and Adriana Puello Alcázar. "Analysis of Climate Variability in a Time Series of Precipitation and Temperature Data: A Case Study in Cartagena de Indias, Colombia." Water 14, no. 9 (April 24, 2022): 1378. http://dx.doi.org/10.3390/w14091378.

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Anthropogenic climate change is a global trend, hitherto incontrovertible, causing immense social and economic damage. Although the this is evident at the global level, at the local level, there is still debate about the most appropriate analyses to support this fact. This debate is particularly relevant in developing countries, such as Colombia, where there is a significant lack of data at the local level that require analysis and interpretation. Consequently, studies are often superficially conducted to support climate change theory at the local level. However, such studies are then used to design hydraulic infrastructure, with potential catastrophic errors for human and environmental health. In this study, we sought evidence of climate change through an analysis of a series of data on temperature (maximum, mean and minimum), as well as total annual and maximum rainfall in 24 h registered at the Rafael Nuñez Airport station in the city of Cartagena, Colombia, from 1941 to 2015. The hypotheses of homogeneity, trend, stationarity and non-stationarity were analyzed. Problems of non-homogeneity and the presence of periodicity in the analyzed series were found, showing a trend and apparent non-stationarity in the original series. This could be associated with the effects of climate change. In this case, no correlation was found between temperatures and rainfall. Spectral analysis was performed for all series, and residual series were generated by extracting the harmonics of greatest significance. It was found that the series data generated from the third harmonic are generally stationary and without trend. Therefore, the trend and non-stationarity of the original series are due to problems of non-homogeneity and periodicity in the series. In the results of the stationarity test conducted according to the Phillips–Perron criterion, all series were non-stationary. For the two additional criteria of stationarity tests, 40% were shown to be stationary, and 60% were non-stationary. Specifically, non-homogeneity problems and apparent trends associated with climate change could have negative implications for the design of drainage systems.

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14

Arrieta-Pastrana, Alfonso, Manuel Saba, and Adriana Puello Alcázar. "Analysis of Climate Variability in a Time Series of Precipitation and Temperature Data: A Case Study in Cartagena de Indias, Colombia." Water 14, no. 9 (April 24, 2022): 1378. http://dx.doi.org/10.3390/w14091378.

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Anthropogenic climate change is a global trend, hitherto incontrovertible, causing immense social and economic damage. Although the this is evident at the global level, at the local level, there is still debate about the most appropriate analyses to support this fact. This debate is particularly relevant in developing countries, such as Colombia, where there is a significant lack of data at the local level that require analysis and interpretation. Consequently, studies are often superficially conducted to support climate change theory at the local level. However, such studies are then used to design hydraulic infrastructure, with potential catastrophic errors for human and environmental health. In this study, we sought evidence of climate change through an analysis of a series of data on temperature (maximum, mean and minimum), as well as total annual and maximum rainfall in 24 h registered at the Rafael Nuñez Airport station in the city of Cartagena, Colombia, from 1941 to 2015. The hypotheses of homogeneity, trend, stationarity and non-stationarity were analyzed. Problems of non-homogeneity and the presence of periodicity in the analyzed series were found, showing a trend and apparent non-stationarity in the original series. This could be associated with the effects of climate change. In this case, no correlation was found between temperatures and rainfall. Spectral analysis was performed for all series, and residual series were generated by extracting the harmonics of greatest significance. It was found that the series data generated from the third harmonic are generally stationary and without trend. Therefore, the trend and non-stationarity of the original series are due to problems of non-homogeneity and periodicity in the series. In the results of the stationarity test conducted according to the Phillips–Perron criterion, all series were non-stationary. For the two additional criteria of stationarity tests, 40% were shown to be stationary, and 60% were non-stationary. Specifically, non-homogeneity problems and apparent trends associated with climate change could have negative implications for the design of drainage systems.

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15

FELLNER, KLEMENS, and GAËL RAOUL. "STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS." Mathematical Models and Methods in Applied Sciences 20, no. 12 (December 2010): 2267–91. http://dx.doi.org/10.1142/s0218202510004921.

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In this paper, we are interested in the large-time behaviour of a solution to a non-local interaction equation, where a density of particles/individuals evolves subject to an interaction potential and an external potential. It is known that for regular interaction potentials, stable stationary states of these equations are generically finite sums of Dirac masses. For a finite sum of Dirac masses, we give (i) a condition to be a stationary state, (ii) two necessary conditions of linear stability w.r.t. shifts and reallocations of individual Dirac masses, and (iii) show that these linear stability conditions imply local non-linear stability. Finally, we show that for regular repulsive interaction potential Wε converging to a singular repulsive interaction potential W, the Dirac-type stationary states [Formula: see text] approximate weakly a unique stationary state [Formula: see text]. We illustrate our results with numerical examples.

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16

Li, Fang, Wei Chen, and Yishui Shui. "Analysis of Non-Stationarity for 5.9 GHz Channel in Multiple Vehicle-to-Vehicle Scenarios." Sensors 21, no. 11 (May 23, 2021): 3626. http://dx.doi.org/10.3390/s21113626.

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The vehicle-to-vehicle (V2V) radio channel is non-stationary due to the rapid movement of vehicles. However, the stationarity of the V2V channels is an important indicator of the V2V channel characteristics. Therefore, we analyzed the non-stationarity of V2V radio channels using the local region of stationarity (LRS). We selected seven scenarios, including three directions of travel, i.e., in the same, vertical, and opposite directions, and different speeds and environments in a similar driving direction. The power delay profile (PDP) and LRS were estimated from the measured channel impulse responses. The results show that the most important influences on the stationary times are the direction and the speed of the vehicles. The average stationary times for driving in the same direction range from 0.3207 to 1.9419 s, the average stationary times for driving in the vertical direction are 0.0359–0.1348 s, and those for driving in the opposite direction are 0.0041–0.0103 s. These results are meaningful for the analysis of the statistical characteristics of the V2V channel, such as the delay spread and Doppler spread. Small-scale fading based on the stationary times affects the quality of signals transmitted in the V2V channel, including the information transmission rate and the information error code rate.

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17

Sergides, Marios, and Efstathios Paparoditis. "Bootstrapping the Local Periodogram of Locally Stationary Processes." Journal of Time Series Analysis 29, no. 2 (March 2008): 264–99. http://dx.doi.org/10.1111/j.1467-9892.2007.00556.x.

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18

Zhao, Zhibiao. "Inference for Local Autocorrelations in Locally Stationary Models." Journal of Business & Economic Statistics 33, no. 2 (August 8, 2014): 296–306. http://dx.doi.org/10.1080/07350015.2014.948177.

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19

Žalys, A. J., and A. A. Tempel’man. "Spatially Stationary Generalized Gaussian Fields with Local Interaction." Theory of Probability & Its Applications 36, no. 1 (January 1992): 197–200. http://dx.doi.org/10.1137/1136023.

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20

Xu, Xiangsheng. "Local regularity theorems for the stationary thermistor problem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 4 (August 2004): 773–82. http://dx.doi.org/10.1017/s0308210500003474.

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In this paper we present a simpler proof of a result of Lewis concerning the continuity of weak solutions to the two-dimensional thermistor problem in the case where the temperature can blow up in a region with non-empty interior. Some other regularity properties are also discussed.

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21

Suzuki, Takashi, and Souhei Tasaki. "Stationary Fix–Caginalp equation with non-local term." Nonlinear Analysis: Theory, Methods & Applications 71, no. 3-4 (August 2009): 1329–49. http://dx.doi.org/10.1016/j.na.2008.12.007.

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22

Rubinacci, G., R. Fresa, and R. Albanese. "Local error bounds for static and stationary fields." IEEE Transactions on Magnetics 36, no. 4 (July 2000): 1615–18. http://dx.doi.org/10.1109/20.877750.

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23

Liakka, Johan, and Johan Nilsson. "The impact of topographically forced stationary waves on local ice-sheet climate." Journal of Glaciology 56, no. 197 (2010): 534–44. http://dx.doi.org/10.3189/002214310792447824.

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AbstractA linear two-level atmospheric model is employed to study the influence of ice-sheet topography on atmospheric stationary waves. In particular, the stationary-wave-induced temperature anomaly is considered locally over a single ice-sheet topography, which is computed using the plastic approximation. It is found that stationary waves induce a local cooling which increases linearly with the ice volume for ice sheets of horizontal extents smaller than ∼1400 km. Beyond this horizontal scale, the dependence of stationary-wave-induced cooling on the ice volume becomes gradually weaker. For a certain ice-sheet size, and for small changes of the surface zonal wind, it is further shown that the strength of the local stationary-wave-induced cooling is proportional to the basic state meridional temperature gradient multiplied by the vertical stratification in the atmosphere. These results are of importance for the nature of the feedback between ice sheets and stationary waves, and may also serve as a basis for parameterizing this feedback in ice-sheet model simulations (e.g. through the Pleistocene glacial/interglacial cycles).

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24

Kozlov, Andrey Nikolaevich, Venyamin Sergeevich Konovalov, and Svetlana Olegovna Novikova. "Study of pulsating flows of ionizing hydrogen in the plasma accelerator based on two-dimensional model." Keldysh Institute Preprints, no. 96 (2021): 1–24. http://dx.doi.org/10.20948/prepr-2021-96.

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Numerical study of the hydrogen ionization process in the channel of the quasi-stationary plasma accelerator is presented. Calculations of pulsating and stationary flows of ionizing hydrogen were carried out within the framework of two-dimensional MHD model in the approximation of local thermodynamic equilibrium, taking into account the radiation transport and under the condition of uniform gas supply at the channel inlet. As a result of a series of calculations, the empirical condition for the stationarity of axisymmetric flows of ionizing hydrogen was determined.

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25

Denker, Manfred, and Xiaofei Zheng. "On the local times of stationary processes with conditional local limit theorems." Stochastic Processes and their Applications 128, no. 7 (July 2018): 2448–62. http://dx.doi.org/10.1016/j.spa.2017.09.012.

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26

Boucherie, Richard J. "On the quasi-stationary distribution for queueing networks with defective routing." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 38, no. 4 (April 1997): 454–63. http://dx.doi.org/10.1017/s0334270000000795.

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AbstractThis note introduces quasi-local-balance for discrete-time Markov chains with absorbing states. From quasi-local-balance product-form quasi-stationary distributions are derived by analogy with product-form stationary distributions for Markov chains that satisfy local balance.

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27

Eskew, Monroe. "Local saturation and square everywhere." Journal of Mathematical Logic 20, no. 03 (March 25, 2020): 2050019. http://dx.doi.org/10.1142/s0219061320500191.

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We show that it is consistent relative to a huge cardinal that for all infinite cardinals [Formula: see text], [Formula: see text] holds and there is a stationary [Formula: see text] such that [Formula: see text] is [Formula: see text]-saturated.

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28

Hu, Junjuan, and Zhenlong Chen. "A unit root test against globally stationary ESTAR models when local condition is non-stationary." Economics Letters 146 (September 2016): 89–94. http://dx.doi.org/10.1016/j.econlet.2016.07.002.

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29

HODYSS, DANIEL, and TERRENCE R. NATHAN. "The role of forcing in the local stability of stationary long waves. Part 1. Linear dynamics." Journal of Fluid Mechanics 576 (March 28, 2007): 349–76. http://dx.doi.org/10.1017/s0022112006004307.

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The local linear stability of forced, stationary long waves produced by topography or potential vorticity (PV) sources is examined using a quasi-geostrophic barotropic model. A multiple scale analysis yields coupled equations for the background stationary wave and low-frequency (LF) disturbance field. Forcing structures for which the LF dynamics are Hamiltonian are shown to yield conservation laws that provide necessary conditions for instability and a constraint on the LF structures that can develop. Explicit knowledge of the forcings that produce the stationary waves is shown to be crucial to predicting a unique LF field. Various topographies or external PV sources can be chosen to produce stationary waves that differ by asymptotically small amounts, yet the LF instabilities that develop can have fundamentally different structures and growth rates. If the stationary wave field is forced solely by topography, LF oscillatory modes always emerge. In contrast, if the stationary wave field is forced solely by PV, two LF structures are possible: oscillatory modes or non-oscillatory envelope modes. The development of the envelope modes within the context of a linear LF theory is novel.An analysis of the complex WKB branch points, which yields an analytical expres-sion for the leading-order eigenfrequency, shows that the streamwise distribution of absolute instability and convective growth is central to understanding and predicting the types of LF structures that develop on the forced stationary wave. The location of the absolute instability region with respect to the stationary wave determines whether oscillatory modes or envelope modes develop. In the absence of absolute instability, eastward propagating wavetrains generated in the far field can amplify via local convective growth in the stationary wave region. If the stationary wave region is streamwise symmetric (asymmetric), the local convective growth results in a local change in wave energy that is transient (permanent).

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30

Carbotti, Alessandro, Serena Dipierro, and Enrico Valdinoci. "Local density of Caputo-stationary functions of any order." Complex Variables and Elliptic Equations 65, no. 7 (December 5, 2018): 1115–38. http://dx.doi.org/10.1080/17476933.2018.1544631.

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31

Ertl, Sabine, Daniel Grumiller, and Niklas Johansson. "All stationary axisymmetric local solutions of topologically massive gravity." Classical and Quantum Gravity 27, no. 22 (October 27, 2010): 225021. http://dx.doi.org/10.1088/0264-9381/27/22/225021.

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32

Obada, A. S. F., H. A. Hessian, A. B. A. Mohamed, and M. Hashem. "Stationary discord and non-local correlations via qubit damping." Journal of Modern Optics 62, no. 11 (March 16, 2015): 918–26. http://dx.doi.org/10.1080/09500340.2015.1015637.

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33

Du, Jian-Ying, and Fu-Lin Zhang. "Perturbative Treatment for Stationary State of Local Master Equation." Communications in Theoretical Physics 70, no. 1 (July 2018): 038. http://dx.doi.org/10.1088/0253-6102/70/1/38.

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34

Escher, Joachim, and Patrick Guidotti. "Local well-posedness for a quasi-stationary droplet model." Calculus of Variations and Partial Differential Equations 54, no. 1 (January 24, 2015): 1147–60. http://dx.doi.org/10.1007/s00526-015-0820-7.

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35

Abed, Eyad H., and Jyun-Horng Fu. "Local feedback stabilization and bifurcation control, II. Stationary bifurcation." Systems & Control Letters 8, no. 5 (May 1987): 467–73. http://dx.doi.org/10.1016/0167-6911(87)90089-2.

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36

Gomes, Diogo A., Levon Nurbekyan, and Mariana Prazeres. "One-Dimensional Stationary Mean-Field Games with Local Coupling." Dynamic Games and Applications 8, no. 2 (May 25, 2017): 315–51. http://dx.doi.org/10.1007/s13235-017-0223-9.

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37

Shioya, Masahiro, and Naoki Yamaura. "Local weak presaturation of the strongly non‐stationary ideal." Mathematical Logic Quarterly 66, no. 1 (March 2020): 99–103. http://dx.doi.org/10.1002/malq.201900033.

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38

Usuba, Toshimichi. "Local saturation of the non-stationary ideal over Pκλ." Annals of Pure and Applied Logic 149, no. 1-3 (November 2007): 100–123. http://dx.doi.org/10.1016/j.apal.2007.08.002.

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39

QILIN, LIU, LIANG FEI, and LI YUXIANG. "Asymptotic behaviour for a non-local parabolic problem." European Journal of Applied Mathematics 20, no. 3 (June 2009): 247–67. http://dx.doi.org/10.1017/s0956792509007803.

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In this paper, we consider the asymptotic behaviour for the non-local parabolic problemwith a homogeneous Dirichlet boundary condition, where λ > 0,p> 0 andfis non-increasing. It is found that (a) for 0 <p≤ 1,u(x,t) is globally bounded and the unique stationary solution is globally asymptotically stable for any λ > 0; (b) for 1 <p< 2,u(x,t) is globally bounded for any λ > 0; (c) forp= 2, if 0 < λ < 2|∂Ω|2, thenu(x,t) is globally bounded; if λ = 2|∂Ω|2, there is no stationary solution andu(x,t) is a global solution andu(x,t) → ∞ ast→ ∞ for allx∈ Ω; if λ > 2|∂Ω|2, there is no stationary solution andu(x,t) blows up in finite time for allx∈ Ω; (d) forp> 2, there exists a λ* > 0 such that for λ > λ*, or for 0 < λ ≤ λ* andu0(x) sufficiently large,u(x,t) blows up in finite time. Moreover, some formal asymptotic estimates for the behaviour ofu(x,t) as it blows up are obtained forp≥ 2.

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40

Lin, Jin Shan. "Fault Diagnosis of Offshore Platforms Using the Local Mean Decomposition Method." Advanced Materials Research 365 (October 2011): 94–97. http://dx.doi.org/10.4028/www.scientific.net/amr.365.94.

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Traditional techniques are not suitable for exploring non-stationary and nonlinear signals. Although empirical mode decomposition (EMD) is a powerful tool for the non-stationary and nonlinear signal analysis, yet it still has some shortcomings. Local mean decomposition (LMD), a novel signal processing method, seemingly overcomes many deficiencies of the EMD method and can take place of the EMD method for analyzing non-stationary and nonlinear signals. In this paper, the LMD method is employed to examine the signal captured from the decks of the WZ12-1 platform and succeeds in displaying the reasons causing the excessive vibration of the WZ12-1 platform. The results suggest that the LMD method seems to be a feasible method for fault diagnosis of offshore platforms.

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41

Seleznjev, Oleg. "Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments." Advances in Applied Probability 28, no. 2 (June 1996): 481–99. http://dx.doi.org/10.2307/1428068.

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We consider the piecewise linear interpolation of Gaussian processes with continuous sample paths and stationary increments. The interrelation between the smoothness of the incremental variance function, d(t – s) = E[(X(t) – X(s))2], and the interpolation errors in mean square and uniform metrics is studied. The method of investigation can also be applied to the analysis of different methods of interpolation. It is based on some limit results for large deviations of a sequence of Gaussian non-stationary processes and related point processes. Non-stationarity in our case means mainly the local stationary condition for the sequence of correlation functions rn(t,s), n = 1, 2, ···, which has to hold uniformly in n. Finally, we discuss some examples and an application to the calculation of the distribution function of the maximum of a continuous Gaussian process with a given precision.

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42

Seleznjev, Oleg. "Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments." Advances in Applied Probability 28, no. 02 (June 1996): 481–99. http://dx.doi.org/10.1017/s0001867800048588.

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We consider the piecewise linear interpolation of Gaussian processes with continuous sample paths and stationary increments. The interrelation between the smoothness of the incremental variance function, d(t – s) = E[(X(t) – X(s))2], and the interpolation errors in mean square and uniform metrics is studied. The method of investigation can also be applied to the analysis of different methods of interpolation. It is based on some limit results for large deviations of a sequence of Gaussian non-stationary processes and related point processes. Non-stationarity in our case means mainly the local stationary condition for the sequence of correlation functions rn(t, s), n = 1, 2, ···, which has to hold uniformly in n. Finally, we discuss some examples and an application to the calculation of the distribution function of the maximum of a continuous Gaussian process with a given precision.

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43

Massopust, Peter. "Non-Stationary Fractal Interpolation." Mathematics 7, no. 8 (July 25, 2019): 666. http://dx.doi.org/10.3390/math7080666.

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We introduce the novel concept of a non-stationary iterated function system by considering a countable sequence of distinct set-valued maps { F k } k ∈ N where each F k maps H ( X ) → H ( X ) and arises from an iterated function system. Employing the recently-developed theory of non-stationary versions of fixed points and the concept of forward and backward trajectories, we present new classes of fractal functions exhibiting different local and global behavior and extend fractal interpolation to this new, more flexible setting.

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BOCCARA, N., and M. ROGER. "SOME PROPERTIES OF LOCAL AND NONLOCAL SITE EXCHANGE DETERMINISTIC CELLULAR AUTOMATA." International Journal of Modern Physics C 05, no. 03 (June 1994): 581–88. http://dx.doi.org/10.1142/s0129183194000751.

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Stationary densities of nonzero sites of one-dimensional range-one deterministic cellular automata are shown to be functions of a parameter m characterizing the degree of mixing of site values. The mixing results from either a local or a nonlocal exchange of the site values. In particular, the asymptotic behavior of the stationary densities of nonzero sites for very small and very large values of the parameter m have been determined.

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45

Kuusela, Mikael, and Michael L. Stein. "Locally stationary spatio-temporal interpolation of Argo profiling float data." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2220 (December 2018): 20180400. http://dx.doi.org/10.1098/rspa.2018.0400.

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Argo floats measure seawater temperature and salinity in the upper 2000 m of the global ocean. Statistical analysis of the resulting spatio-temporal dataset is challenging owing to its non-stationary structure and large size. We propose mapping these data using locally stationary Gaussian process regression where covariance parameter estimation and spatio-temporal prediction are carried out in a moving-window fashion. This yields computationally tractable non-stationary anomaly fields without the need to explicitly model the non-stationary covariance structure. We also investigate Student t -distributed fine-scale variation as a means to account for non-Gaussian heavy tails in ocean temperature data. Cross-validation studies comparing the proposed approach with the existing state of the art demonstrate clear improvements in point predictions and show that accounting for the non-stationarity and non-Gaussianity is crucial for obtaining well-calibrated uncertainties. This approach also provides data-driven local estimates of the spatial and temporal dependence scales for the global ocean, which are of scientific interest in their own right.

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Lv, Jinman, Zhenhua Peng, and Zhongping Wan. "Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints." Mathematics 9, no. 22 (November 16, 2021): 2915. http://dx.doi.org/10.3390/math9222915.

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In this paper, we consider a class of mathematical programs with switching constraints (MPSCs) where the objective involves a non-Lipschitz term. Due to the non-Lipschitz continuity of the objective function, the existing constraint qualifications for local Lipschitz MPSCs are invalid to ensure that necessary conditions hold at the local minimizer. Therefore, we propose some MPSC-tailored qualifications which are related to the constraints and the non-Lipschitz term to ensure that local minimizers satisfy the necessary optimality conditions. Moreover, we study the weak, Mordukhovich, Bouligand, strongly (W-, M-, B-, S-) stationay, analyze what qualifications making local minimizers satisfy the (M-, B-, S-) stationay, and discuss the relationship between the given MPSC-tailored qualifications. Finally, an approximation method for solving the non-Lipschitz MPSCs is given, and we show that the accumulation point of the sequence generated by the approximation method satisfies S-stationary under the second-order necessary condition and MPSC Mangasarian-Fromovitz (MF) qualification.

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47

Gerbino, Walter, and Nicola Bruno. "Paradoxical Rest." Perception 26, no. 12 (December 1997): 1549–54. http://dx.doi.org/10.1068/p261549.

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Paradoxical absence of motion in a rotating pattern is reported. The effect requires that the motion of the paradoxically stationary figure be underspecified by local motion signals, and that the paradoxically stationary figure be well segregated. This is consistent with proposals that figural segregation affects the integration of local motion signals.

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Konstantopoulos, Takis. "A local proof of the Swiss Army formula of Palm calculus." Journal of Applied Probability 33, no. 3 (September 1996): 909–14. http://dx.doi.org/10.2307/3215368.

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The so-called ‘Swiss Army formula', derived by Brémaud, seems to be a general purpose relation which includes all known relations of Palm calculus for stationary stochastic systems driven by point processes. The purpose of this article is to present a short, and rather intuitive, proof of the formula. The proof is based on the Ryll–Nardzewski definition of the Palm probability as a Radon-Nikodym derivative, which, in a stationary context, is equivalent to the Mecke definition.

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Konstantopoulos, Takis. "A local proof of the Swiss Army formula of Palm calculus." Journal of Applied Probability 33, no. 03 (September 1996): 909–14. http://dx.doi.org/10.1017/s0021900200100300.

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The so-called ‘Swiss Army formula', derived by Brémaud, seems to be a general purpose relation which includes all known relations of Palm calculus for stationary stochastic systems driven by point processes. The purpose of this article is to present a short, and rather intuitive, proof of the formula. The proof is based on the Ryll–Nardzewski definition of the Palm probability as a Radon-Nikodym derivative, which, in a stationary context, is equivalent to the Mecke definition.

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50

Yang, Lin. "Application of Local Wave Method in the Structural Health Monitoring Signal Decomposition." Applied Mechanics and Materials 457-458 (October 2013): 969–73. http://dx.doi.org/10.4028/www.scientific.net/amm.457-458.969.

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Health monitoring of the bridge structure has gradually become one of the hot topics. The signal decomposition technology is the key technique of the bridge structural health monitoring. The traditional data analysis and processing methods, which can only be applied to stationary or linear signal processing, have significant limitations. However, the structural response signals tested are mostly non-stationary and nonlinear. So methods that can effectively analyze non-stationary and nonlinear signal are urgently needed. Based on the summarization and analysis of the shortage of wavelet analysis method, the application of local wave method for data processing and analysis in structural health monitoring is put forward. The feasibility and superiority of local wave method is discussed. Experimental simulation results show that the application of local wave method in bridge health monitoring signal decomposition is feasible.

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