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Journal articles on the topic 'Piecewise stationarity'

Author: Grafiati

Published: 8 June 2024

Last updated: 31 July 2025

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1

Prasolov, Aleksander V., Nikita G. Ivanov, and Nikolay V. Smirnov. "Algorithm of variance estimation in weighted least squares method." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 19, no. 4 (2023): 484–96. http://dx.doi.org/10.21638/11701/spbu10.2023.405.

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The representation of a time series model as a piecewise-stationary process is provided, wherein it is regarded as a collection of successive stationary intervals. An algorithm has been developed for identifying the domain containing the trend within this model. It is recognized that applying the least squares method directly for trend determination is not commonly employed in statistical analysis and econometric software packages. Typically, the weighted least squares method is utilized to ideally eliminate non-stationarity. The authors presents an algorithm for estimating the weight coeffici

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2

Fell, Jürgen, Alexander Kaplan, Boris Darkhovsky, and Joachim Röschke. "EEG analysis with nonlinear deterministic and stochastic methods: a combined strategy." Acta Neurobiologiae Experimentalis 60, no. 1 (2000): 87–108. http://dx.doi.org/10.55782/ane-2000-1328.

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We describe nonlinear deterministic versus stochastic methodology, their applications to EEG research and the neurophysiological background underlying both approaches. Nonlinear methods are based on the concept of attractors in phase space. This concept on the one hand incorporates the idea of an autonomous (stationary) system, on the other hand implicates the investigation of a long time evolution. It is an unresolved problem in nonlinear EEG research that nonlinear methods per se give no feedback about the stationarity aspect. Hence, we introduce a combined strategy utilizing both stochastic

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3

Seleznjev, Oleg. "Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments." Advances in Applied Probability 28, no. 2 (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

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Seleznjev, Oleg. "Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments." Advances in Applied Probability 28, no. 02 (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

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5

Dorovskikh, Dmitriy I., Alexey F. Izmailov, and Evgeniy I. Uskov. "Globalizing convergence of piecewise Newton methods." Russian Universities Reports. Mathematics, no. 146 (2024): 149–63. http://dx.doi.org/10.20310/2686-9667-2024-29-146-149-163.

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We consider versions of the Newton method for piecewise smooth nonlinear equations, as well as of the Gauss–Newton method for the case when additional constraints are imposed, supplied with linesearch procedures for the residual of the equation, aiming at globalization of convergence. (Constrained) piecewise smooth nonlinear equations arise naturally as reformulations of systems of equations and inequalities involving complementarity conditions. In cases when the direction of the Newton method cannot be computed, or appears too long, the algorithm switches to a safeguarding step of the gradien

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6

PODIO-GUIDUGLI, PAOLO, and GIORGIO VERGARA CAFFARELLI. "EQUILIBRIUM PHASES AND LAYERED PHASE MIXTURES IN ELASTICITY." Mathematical Models and Methods in Applied Sciences 02, no. 02 (1992): 143–66. http://dx.doi.org/10.1142/s0218202592000107.

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In this paper an equilibrium phase is a restriction of a piecewise-affine deformation of a body to a (maximal, connected) subbody whose deformation is affine; a layered phase mixture is a continuous deformation that admits at least two distinct phases, separated by a plane interface. We study equilibrium phases and layered phase mixtures in the context of finite elasticity, in the presence of three different boundary conditions of traction: uniform pressure, and two other of null Lagrangians. In Part I we reduce to a unique format the stationarity condition for the existence of equilibrium pha

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Moltchanov, D. "Modeling local stationary behavior of Internet traffic." Journal of Communications Software and Systems 4, no. 1 (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 m

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8

Rosenthal, Jeffrey S. "Random walks on discrete and continuous circles." Journal of Applied Probability 30, no. 4 (1993): 780–89. http://dx.doi.org/10.2307/3214512.

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We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S1.

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Rosenthal, Jeffrey S. "Random walks on discrete and continuous circles." Journal of Applied Probability 30, no. 04 (1993): 780–89. http://dx.doi.org/10.1017/s0021900200044569.

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We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S 1.

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10

van der Baan, Mirko, and Sergey Fomel. "Nonstationary phase estimation using regularized local kurtosis maximization." GEOPHYSICS 74, no. 6 (2009): A75—A80. http://dx.doi.org/10.1190/1.3213533.

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Phase mismatches sometimes occur between final processed seismic sections and zero-phase synthetics based on well logs — despite best efforts for controlled-phase acquisition and processing. Statistical estimation of the phase of a seismic wavelet is feasible using kurtosis maximization by constant-phase rotation, even if the phase is nonstationary. We cast the phase-estimation problem into an optimization framework to improve the stability of an earlier method based on a piecewise-stationarity assumption. After estimation, we achieve space-and-time-varying zero-phasing by phase rotation.

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11

NAKATSUJI, Takashi, and Terutoshi KAKU. "IMPROVEMENT OF PREDICTION SCHEME OF TRAFFIC FLOW ON URBAN STREETS BASED ON PIECEWISE STATIONARITY." INFRASTRUCTURE PLANNING REVIEW 4 (1986): 101–8. http://dx.doi.org/10.2208/journalip.4.101.

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12

Dong, Li, Jiantao Zhou, and Yuan Yan Tang. "Noise Level Estimation for Natural Images Based on Scale-Invariant Kurtosis and Piecewise Stationarity." IEEE Transactions on Image Processing 26, no. 2 (2017): 1017–30. http://dx.doi.org/10.1109/tip.2016.2639447.

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13

Echavarria-Heras, Héctor A., Cecilia Leal-Ramírez, Guillermo Gómez, and Elia Montiel-Arzate. "Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics." Complexity 2021 (December 27, 2021): 1–24. http://dx.doi.org/10.1155/2021/5623783.

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We examine the comportment of the global trajectory of a piecewisely conceived single species population growth model. Formulation relies on what we develop as the principle of limiting factors for population growth, adapted from the law of the minimum of Liebig and the law of the tolerance of Shelford. The ensuing paradigm sets natality and mortality rates to express through extreme values of population growth determining factor. Dynamics through time occur over different growth phases. Transition points are interpreted as thresholds of viability, starvation, and intraspecific competition. In

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14

Luo, Yuwei, Varun Gupta, and Mladen Kolar. "Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systems." ACM SIGMETRICS Performance Evaluation Review 50, no. 1 (2022): 75–76. http://dx.doi.org/10.1145/3547353.3522649.

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We consider the problem of controlling a Linear Quadratic Regulator (LQR) system over a finite horizon T with fixed and known cost matrices Q,R, but unknown and non-stationary dynamics At, Bt. The sequence of dynamics matrices can be arbitrary, but with a total variation, VT, assumed to be o(T) and unknown to the controller. Under the assumption that a sequence of stabilizing, but potentially sub-optimal controllers is available for all t, we present an algorithm that achieves the optimal dynamic regret of Õ(VT2/5 T3/5). With piecewise constant dynamics, our algorithm achieves the optimal regr

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Luo, Yuwei, Varun Gupta, and Mladen Kolar. "Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systems." Proceedings of the ACM on Measurement and Analysis of Computing Systems 6, no. 1 (2022): 1–72. http://dx.doi.org/10.1145/3508029.

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We consider the problem of controlling a Linear Quadratic Regulator (LQR) system over a finite horizon T with fixed and known cost matrices Q,R, but unknown and non-stationary dynamics A_t, B_t. The sequence of dynamics matrices can be arbitrary, but with a total variation, V_T, assumed to be o(T) and unknown to the controller. Under the assumption that a sequence of stabilizing, but potentially sub-optimal controllers is available for all t, we present an algorithm that achieves the optimal dynamic regret of O(V_T^2/5 T^3/5 ). With piecewise constant dynamics, our algorithm achieves the optim

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Kumar, Jitendra, Varun Varun, Dhirendra Kumar, and Anoop Chaturvedi. "Bayesian Unit Root Test for AR(1) Model with Trend Approximated." Statistics, Optimization & Information Computing 8, no. 2 (2020): 425–61. http://dx.doi.org/10.19139/soic-2310-5070-786.

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The objective of present study is to develop a time series model for handling the non-linear trend process using a spline function. Spline function is a piecewise polynomial segment concerning the time component. The main advantage of spline function is the approximation, non linear time trend, but linear time trend between the consecutive join points. A unit root hypothesis is projected to test the non stationarity due to presence of unit root in the proposed model. In the autoregressive model with linear trend, the time trend vanishes under the unit root case. However, when non-linear trend

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17

Qin, Panke, Yongjie Ding, Ya Li, et al. "Spiking Neural Networks Optimized by Improved Cuckoo Search Algorithm: A Model for Financial Time Series Forecasting." Algorithms 18, no. 5 (2025): 262. https://doi.org/10.3390/a18050262.

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Financial Time Series Forecasting (TSF) remains a critical challenge in Artificial Intelligence (AI) due to the inherent complexity of financial data, characterized by strong non-linearity, dynamic non-stationarity, and multi-factor coupling. To address the performance limitations of Spiking Neural Networks (SNNs) caused by hyperparameter sensitivity, this study proposes an SNN model optimized by an Improved Cuckoo Search (ICS) algorithm (termed ICS-SNN). The ICS algorithm enhances global search capability through piecewise-mapping-based population initialization and introduces a dynamic disco

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18

Mamtiyev, Kamil, Tarana Aliyeva, and Ulviyye Rzayeva. "Solution of one optimum control problem regarding the depletion of gas reservoir." Eastern-European Journal of Enterprise Technologies 1, no. 4 (115) (2022): 6–13. http://dx.doi.org/10.15587/1729-4061.2022.252743.

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Using the methods of the optimal control theory, the problem of determining the optimal technological mode of gas deposits’ exploitation under the condition of their depletion by a given point in time is solved. This task is of particular interest for the exploitation of offshore fields, the activity of which is limited by the service life of the field equipment. The considered problem is also of certain mathematical interest as an objective of optimal control of nonlinear systems with distributed parameters. The usefulness and importance of solving such problems are determined by the richness

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Kamil, Mamtiyev, Aliyeva Tarana, and Rzayeva Ulviyye. "Solution of one optimum control problem regarding the depletion of gas reservoir." Eastern-European Journal of Enterprise Technologies 1, no. 4 (115) (2022): 6–13. https://doi.org/10.15587/1729-4061.2022.252743.

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Using the methods of the optimal control theory, the problem of determining the optimal technological mode of gas deposits’ exploitation under the condition of their depletion by a given point in time is solved. This task is of particular interest for the exploitation of offshore fields, the activity of which is limited by the service life of the field equipment. The considered problem is also of certain mathematical interest as an objective of optimal control of nonlinear systems with distributed parameters. The usefulness and importance of solving such problems are determined by the ri

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20

LEE, AN-CHEN, and JIING-SHYANG CHOU. "Segmentation of piecewise stationary signals." International Journal of Systems Science 20, no. 10 (1989): 1827–42. http://dx.doi.org/10.1080/00207728908910268.

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21

Zhou, Huozhi, Lingda Wang, Lav Varshney, and Ee-Peng Lim. "A Near-Optimal Change-Detection Based Algorithm for Piecewise-Stationary Combinatorial Semi-Bandits." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 6933–40. http://dx.doi.org/10.1609/aaai.v34i04.6176.

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We investigate the piecewise-stationary combinatorial semi-bandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-stationary manner at unknown time steps. We propose an algorithm, GLR-CUCB, which incorporates an efficient combinatorial semi-bandit algorithm, CUCB, with an almost parameter-free change-point detector, the Generalized Likelihood Ratio Test (GLRT). Our analysis shows that the regret of GLR-CUCB is upper bounded by O(√NKT log T), where N is the number of piecewise-stationary seg

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22

Costa, O. L. V. "Stationary distributions for piecewise-deterministic Markov processes." Journal of Applied Probability 27, no. 1 (1990): 60–73. http://dx.doi.org/10.2307/3214595.

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In this paper we show that the problem of existence and uniqueness of stationary distributions for piecewise-deterministic Markov processes (PDPs) is equivalent to the same problem for the associated Markov chain, so long as some mild conditions on the parameters of the PDP are satisfied. Our main result is the construction of an invertible mapping from the set of stationary distributions for the PDP to the set of stationary distributions for the Markov chain. Some sufficient conditions for existence are presented and an application to capacity expansion is given.

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Costa, O. L. V. "Stationary distributions for piecewise-deterministic Markov processes." Journal of Applied Probability 27, no. 01 (1990): 60–73. http://dx.doi.org/10.1017/s0021900200038420.

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In this paper we show that the problem of existence and uniqueness of stationary distributions for piecewise-deterministic Markov processes (PDPs) is equivalent to the same problem for the associated Markov chain, so long as some mild conditions on the parameters of the PDP are satisfied. Our main result is the construction of an invertible mapping from the set of stationary distributions for the PDP to the set of stationary distributions for the Markov chain. Some sufficient conditions for existence are presented and an application to capacity expansion is given.

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24

Xu, Pengfei, and Yinjie Jia. "SNR improvement based on piecewise linear interpolation." Journal of Electrical Engineering 72, no. 5 (2021): 348–51. http://dx.doi.org/10.2478/jee-2021-0049.

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Abstract Interpolation improves the resolution of the curve. Based on the stationary characteristics of the signal and the non-stationary characteristics of the noise, the theoretical proof indicates that the piecewise linear interpolation can improve the signal-to-noise ratio, which is further confirmed by simulation results.

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Morgan, Matthew R., Gregg E. Trahey, and William F. Walker. "Speckle coherence of piecewise-stationary stochastic targets." Journal of the Acoustical Society of America 146, no. 3 (2019): 1721–31. http://dx.doi.org/10.1121/1.5126686.

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26

Begovatov, E. A., and N. P. Evlampiev. "Correlation function of a piecewise-stationary process." Journal of Soviet Mathematics 45, no. 2 (1989): 1084–88. http://dx.doi.org/10.1007/bf01095706.

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27

BOFFI, D. "STABILITY OF HIGHER ORDER TRIANGULAR HOOD-TAYLOR METHODS FOR THE STATIONARY STOKES EQUATIONS." Mathematical Models and Methods in Applied Sciences 04, no. 02 (1994): 223–35. http://dx.doi.org/10.1142/s0218202594000133.

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We prove the stability for the approximation of the stationary Stokes equations by means of piecewise continuous velocities of degree k+1 and piecewise continuous pressures of degree k for k≥1. The necessary and sufficient condition required on the triangulation is that it contains at least three triangles. The theorem is compared with previous results.

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28

Koldovský, Zbyněk, Jiří Málek, Petr Tichavský, Yannick Deville, and Shahram Hosseini. "Blind separation of piecewise stationary non-Gaussian sources." Signal Processing 89, no. 12 (2009): 2570–84. http://dx.doi.org/10.1016/j.sigpro.2009.04.021.

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29

Fujii, Takayuki. "Nonparametric Estimation for a Class of Piecewise-Deterministic Markov Processes." Journal of Applied Probability 50, no. 4 (2013): 931–42. http://dx.doi.org/10.1239/jap/1389370091.

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In this paper we study nonparametric estimation problems for a class of piecewise-deterministic Markov processes (PDMPs). Borovkov and Last (2008) proved a version of Rice's formula for PDMPs, which explains the relation between the stationary density and the level crossing intensity. From a statistical point of view, their result suggests a methodology for estimating the stationary density from observations of a sample path of PDMPs. First, we introduce the local time related to the level crossings and construct the local-time estimator for the stationary density, which is unbiased and unifor

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Fujii, Takayuki. "Nonparametric Estimation for a Class of Piecewise-Deterministic Markov Processes." Journal of Applied Probability 50, no. 04 (2013): 931–42. http://dx.doi.org/10.1017/s0021900200013711.

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In this paper we study nonparametric estimation problems for a class of piecewise-deterministic Markov processes (PDMPs). Borovkov and Last (2008) proved a version of Rice's formula for PDMPs, which explains the relation between the stationary density and the level crossing intensity. From a statistical point of view, their result suggests a methodology for estimating the stationary density from observations of a sample path of PDMPs. First, we introduce the local time related to the level crossings and construct the local-time estimator for the stationary density, which is unbiased and unifor

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31

Fan, Zhi Ping, Tian Sheng Hong, Zhi Zhuan Liu, and Zheng Zhe Jing. "Improve the Envelope of EMD with Piecewise Linear Fractal Interpolation." Key Engineering Materials 439-440 (June 2010): 390–95. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.390.

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Empirical mode decomposition (EMD) has recently been pioneered by Huang et al. for adaptively representing non-stationary signals as sums of zero-mean amplitude modulation frequency modulation components. The traditional EMD algorithm adopts the cubic spline interpolation as an effective tool processing non-stationary signal, but it cannot effectively extract the characteristic frequencies from a highly non-stationary signal, and the overshoots and the undershoots may become a common phenomenon during the decomposition process. In order to solve the problem, we presents the piecewise linear fr

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32

Sireteanu, Tudor, Ana-Maria Mitu, Ovidiu Solomon, and Marius Giuclea. "Approximation of the Statistical Characteristics of Piecewise Linear Systems with Asymmetric Damping and Stiffness under Stationary Random Excitation." Mathematics 10, no. 22 (2022): 4275. http://dx.doi.org/10.3390/math10224275.

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In this paper, the dynamic response of piecewise linear systems with asymmetric damping and stiffness for random excitation is studied. In order to approximate the statistical characteristics for each significant output of piecewise linear system, a method based on transmissibility factors is applied. A stochastic linear system with the same transmissibility factor is attached, and the statistical parameters of the studied output corresponding to random excitation having rational spectral densities are determined by solving the associated Lyapunov equation. Using the attached linear systems fo

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CHENG, Hao, Guo-qing LIU, and Xiao-gang CHENG. "Approximation model of piecewise stationary stochastic process autocorrelation function." Journal of Computer Applications 32, no. 2 (2013): 589–91. http://dx.doi.org/10.3724/sp.j.1087.2012.00589.

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Borovkov, K., and G. Last. "On Rice's Formula for Stationary Multivariate Piecewise Smooth Processes." Journal of Applied Probability 49, no. 2 (2012): 351–63. http://dx.doi.org/10.1239/jap/1339878791.

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Let X = {Xt: t ≥ 0} be a stationary piecewise continuous Rd-valued process that moves between jumps along the integral curves of a given continuous vector field, and let S ⊂ Rd be a smooth surface. The aim of this paper is to derive a multivariate version of Rice's formula, relating the intensity of the point process of (localized) continuous crossings of S by X to the distribution of X0. Our result is illustrated by examples relating to queueing networks and stress release network models.

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Borovkov, K., and G. Last. "On Rice's Formula for Stationary Multivariate Piecewise Smooth Processes." Journal of Applied Probability 49, no. 02 (2012): 351–63. http://dx.doi.org/10.1017/s002190020000913x.

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LetX= {Xt:t≥ 0} be a stationary piecewise continuousRd-valued process that moves between jumps along the integral curves of a given continuous vector field, and letS⊂Rdbe a smooth surface. The aim of this paper is to derive a multivariate version of Rice's formula, relating the intensity of the point process of (localized) continuous crossings ofSbyXto the distribution ofX0. Our result is illustrated by examples relating to queueing networks and stress release network models.

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吴, 楠. "Multiple Change-Points Detection of Piecewise Stationary Time Series." Pure Mathematics 08, no. 02 (2018): 136–48. http://dx.doi.org/10.12677/pm.2018.82018.

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ALIEV, A. B., A. N. HUSEYNOVA, and G. A. ALIYEV. "A MIXED PROBLEM FOR A ONE-DIMENSIONAL VISCOELASTICITY EQUATION WITH NON-STATIONARY CONJUGATION CONDITIONS." Baku Mathematical Journal 1, no. 1 (2022): 63–77. http://dx.doi.org/10.32010/j.bmj.2022.07.

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The problem of a longitudinal impact on a piecewise homogeneous semiinfinite rod consisting of viscoelastic parts is studied. Introducing non-stationary dynamic regularization under conjugation conditions, we prove the well-posedness of the problem under consideration

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Freimanis, Juris. "Polarized radiative transfer equation in some nontrivial coordinate systems." Proceedings of the International Astronomical Union 7, S283 (2011): 360–61. http://dx.doi.org/10.1017/s1743921312011428.

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AbstractExplicit expressions for the differential operator of stationary quasi-monochromatic polarized radiative transfer equation in Euclidean space with piecewise homogeneous real part of the effective refractive index are obtained in circular cylindrical, prolate spheroidal, elliptic conical, classic toroidal and simple toroidal coordinate system.

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Zhang, Lu, Wenqi Wu, and Maosong Wang. "Rapid SINS Two-Position Ground Alignment Scheme Based on Piecewise Combined Kalman Filter and Azimuth Constraint Information." Sensors 19, no. 5 (2019): 1125. http://dx.doi.org/10.3390/s19051125.

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The accuracy and rate of convergence are two important performance factors for initial ground alignment of a strapdown inertial navigation system (SINS). For navigation-grade SINS, gyro biases and accelerometer offsets can be modeled as constant values during the alignment period, and they can be calibrated through two-position ground alignment schemes. In many situations for SINS ground alignment, the azimuth of the vehicle remains nearly constant. This quasi-stationary alignment information can be used as an augmented measurement. In this paper, a piecewise combined Kalman filter utilizing r

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Liu, Zhenxin, and Zhe Wang. "Wasserstein convergence rates in the invariance principle for sequential dynamical systems." Nonlinearity 37, no. 12 (2024): 125019. http://dx.doi.org/10.1088/1361-6544/ad8c1d.

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Abstract In this paper, we consider the convergence rate with respect to the Wasserstein distance in the invariance principle for sequential dynamical systems. We utilize and modify the techniques previously employed for stationary sequences to address our non-stationary case. Under certain assumptions, we can apply our result to a class of dynamical systems, including sequential β n -transformations, piecewise uniformly expanding maps with additive noise in one-dimensional and multidimensional case, and so on.

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Popov, A. M., and R. M. Valiev. "Infinite Linear Systems M/G/\(\infty\) and Multilinear Systems with M/G/n/0 Losses." Current Journal of Applied Science and Technology 42, no. 31 (2023): 15–20. http://dx.doi.org/10.9734/cjast/2023/v42i314212.

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The method based on the description of the probabilities of states using a non-stationary Poisson flow allows using elementary reasoning to find not only a stationary, but also a non-stationary distribution of the number of requirements in the system. To find a stationary distribution of the number of requirements in queuing systems (QS), the method of introducing additional variables leading to a piecewise linear Markov process is used. The fact of invariance is shown: the stationary probabilities of pi states in queuing systems (QS) M/G/n/0 depend only on the average service time

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Дергунов, Олексій Володимирович, and Ганна Вадимівна Мартинюк. "METHOD FOR CHANGE-POINT DETECTION IN PIECEWISE STATIONARY TIME-SERIES." Information systems, mechanics and control, no. 16 (April 10, 2017): 120–27. http://dx.doi.org/10.20535/2219-3804162017100670.

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Shamir, G. I., and N. Merhav. "Low-complexity sequential lossless coding for piecewise-stationary memoryless sources." IEEE Transactions on Information Theory 45, no. 5 (1999): 1498–519. http://dx.doi.org/10.1109/18.771150.

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Sundararajan, Raanju R., and Mohsen Pourahmadi. "Nonparametric change point detection in multivariate piecewise stationary time series." Journal of Nonparametric Statistics 30, no. 4 (2018): 926–56. http://dx.doi.org/10.1080/10485252.2018.1504943.

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Rho, Yeonwoo, and Xiaofeng Shao. "BOOTSTRAP-ASSISTED UNIT ROOT TESTING WITH PIECEWISE LOCALLY STATIONARY ERRORS." Econometric Theory 35, no. 1 (2018): 142–66. http://dx.doi.org/10.1017/s0266466618000038.

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In unit root testing, a piecewise locally stationary process is adopted to accommodate nonstationary errors that can have both smooth and abrupt changes in second- or higher-order properties. Under this framework, the limiting null distributions of the conventional unit root test statistics are derived and shown to contain a number of unknown parameters. To circumvent the difficulty of direct consistent estimation, we propose to use the dependent wild bootstrap to approximate the nonpivotal limiting null distributions and provide a rigorous theoretical justification for bootstrap consistency.

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Last, Michael, and Robert Shumway. "Detecting abrupt changes in a piecewise locally stationary time series." Journal of Multivariate Analysis 99, no. 2 (2008): 191–214. http://dx.doi.org/10.1016/j.jmva.2007.06.010.

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Zhang, Bo, Guodong Pang, and Bert Zwart. "Refining piecewise stationary approximation for a Markov-regulated fluid queue." ACM SIGMETRICS Performance Evaluation Review 42, no. 2 (2014): 15–17. http://dx.doi.org/10.1145/2667522.2667526.

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NIZHNIK, LEONID P., IRINA L. NIZHNIK, and MARTIN HASLER. "STABLE STATIONARY SOLUTIONS IN REACTION–DIFFUSION SYSTEMS CONSISTING OF A 1-D ARRAY OF BISTABLE CELLS." International Journal of Bifurcation and Chaos 12, no. 02 (2002): 261–79. http://dx.doi.org/10.1142/s0218127402004322.

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In this paper we present the construction of stable stationary solutions in reaction–diffusion systems consisting of a 1-D array of bistable cells with a cubic nonlinearity and with a cubic-like piecewise-linear nonlinearity. Some periodic solutions, kinks, solitons are considered. While it is known that spatial chaos arises in such systems with small coupling constants, we show the existence of spatial chaos for an arbitrary value of the cell coupling constant, in the case of the piecewise-linear nonlinearity. The value of the spatial entropy is found. We also show the existence of stable spa

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Pshenichnov, Sergey, Radan Ivanov, and Maria Datcheva. "Transient Wave Propagation in Functionally Graded Viscoelastic Structures." Mathematics 10, no. 23 (2022): 4505. http://dx.doi.org/10.3390/math10234505.

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Transient wave processes in viscoelastic structures built from functionally graded material (FGM) still remain almost unexplored. In this article, the problem of the propagation of nonstationary longitudinal waves in an infinite viscoelastic layer of a FGM with plane–parallel boundaries is considered. The physical and mechanical parameters of the FGM depend continuously on the transverse coordinate, while the wave process propagates along the same coordinate. The viscoelastic properties of the material are taken into account employing the linear integral Boltzmann–Volterra relations. The visco

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Abramowicz, Konrad, and Oleg Seleznjev. "Piecewise-Multilinear Interpolation of a Random Field." Advances in Applied Probability 45, no. 4 (2013): 945–59. http://dx.doi.org/10.1239/aap/1386857852.

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We consider a piecewise-multilinear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured using the integrated mean square error. Piecewise-multilinear interpolator is defined by N-field observations on a locations grid (or design). We investigate the class of locally stationary random fields whose local behavior is like a fractional Brownian field, in the mean square sense, and find the asymptotic approximation accuracy for a sequence of designs for large N. Moreover, for certain classes of continuous and continuously differentiable fiel

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