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Journal articles on the topic 'Random field solution'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

YU. KHRENNIKOV, A., and S. V. KOZYREV. "ULTRAMETRIC RANDOM FIELD." Infinite Dimensional Analysis, Quantum Probability and Related Topics 09, no. 02 (2006): 199–213. http://dx.doi.org/10.1142/s0219025706002317.

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Gaussian random field on general ultrametric space is introduced as a solution of pseudodifferential stochastic equation. Covariation of the introduced random field is computed with the help of wavelet analysis on ultrametric spaces. Notion of ultrametric Markovianity, which describes independence of contributions to random field from different ultrametric balls is introduced. We show that the random field under investigation satisfies this property.

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2

Angulo, J. M., M. D. Ruiz-Medina, and V. V. Anh. "Estimation and filtering of fractional generalised random fields." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 69, no. 3 (2000): 336–61. http://dx.doi.org/10.1017/s1446788700002500.

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AbstractThis paper considers the estimation and filtering of fractional random fields, of which fractional Brownian motion and fractional Riesz-Bessel motion are important special cases. A least-squares solution to the problem is derived by using the duality theory and covariance factorisation of fractional generalised random fields. The minimum fractional duality order of the information random field leads to the most general class of solutions corresponding to the largest function space where the output random field can be approximated. The second-order properties that define the class of ra

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E., M. Omaba, Nwaeze E., and O. Omenyi L. "On Non-existence of Global Weak-predictable-random-field Solutions to a Class of SHEs." Asian Research Journal of Mathematics 4, no. 2 (2017): 1–14. https://doi.org/10.9734/ARJOM/2017/33317.

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The multiplicative non-linearity term is usually assumed to be globally Lipschitz in most results on SPDEs. This work proves that the solutions fail to exist if the non-linearity term grows faster than linear growth. The global non-existence of the solution occurs for some non-linear conditions on . Some precise conditions for existence and uniqueness of the solutions were stated and we have established that the solutions grow in time at most a precise exponential rate at some time interval; and if the solutions satisfy some non-linear conditions then they cease to exist at some finite time .

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4

Opper, M. "Exact solution to a toy random field model." Journal of Physics A: Mathematical and General 26, no. 16 (1993): L719—L722. http://dx.doi.org/10.1088/0305-4470/26/16/002.

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5

Mac, D. Hung, Stephane Clenet, Jean-Claude Mipo, and Olivier Moreau. "Solution of Static Field Problems With Random Domains." IEEE Transactions on Magnetics 46, no. 8 (2010): 3385–88. http://dx.doi.org/10.1109/tmag.2010.2045358.

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Barnes, T., and G. J. Daniell. "Numerical solution of field theories using random walks." Nuclear Physics B 257 (January 1985): 173–98. http://dx.doi.org/10.1016/0550-3213(85)90342-6.

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7

NOUY, A., and C. SOIZE. "Random field representations for stochastic elliptic boundary value problems and statistical inverse problems." European Journal of Applied Mathematics 25, no. 3 (2014): 339–73. http://dx.doi.org/10.1017/s0956792514000072.

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This paper presents new results allowing an unknown non-Gaussian positive matrix-valued random field to be identified through a stochastic elliptic boundary value problem, solving a statistical inverse problem. A new general class of non-Gaussian positive-definite matrix-valued random fields, adapted to the statistical inverse problems in high stochastic dimension for their experimental identification, is introduced and its properties are analysed. A minimal parameterisation of discretised random fields belonging to this general class is proposed. Using this parameterisation of the general cla

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8

Riera, Rosane, C. M. Chaves, and R. R. dos Santos. "Potts chain in a random field: An exact solution." Physical Review B 31, no. 5 (1985): 3093–99. http://dx.doi.org/10.1103/physrevb.31.3093.

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9

Schwartz, M. "The random-field puzzle. I. Solution by equivalent annealing." Journal of Physics C: Solid State Physics 18, no. 1 (1985): 135–58. http://dx.doi.org/10.1088/0022-3719/18/1/019.

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10

Chyan, Phie, and N. Tri Saptadi. "Pemulihan Citra Berbasis Metode Markov Random Field." JURIKOM (Jurnal Riset Komputer) 9, no. 2 (2022): 218. http://dx.doi.org/10.30865/jurikom.v9i2.3966.

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Image processing and computer vision today are faced with increasing big data applications. Excessive collection of Image data sometimes can have bad quality due to errors at the time of acquisition or at the time of transmission, so for that problem the method is needed to perform image restoration. Image restoration is a process to make improvements to the image with the aim of obtaining a clean image from noise like the original image. Among the methods that can be used in image restoration, Markov Random Field (MRF) based on a probabilistic representation of image processing problems, name

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11

Šamaj, L. "An iterative method of the solution of the random-field Ising model with bimodal random-field distribution." Physica A: Statistical Mechanics and its Applications 145, no. 1-2 (1987): 305–26. http://dx.doi.org/10.1016/0378-4371(87)90254-8.

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12

Balan, Raluca M. "SPDEs with α-Stable Lévy Noise: A Random Field Approach". International Journal of Stochastic Analysis 2014 (4 лютого 2014): 1–22. http://dx.doi.org/10.1155/2014/793275.

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This paper is dedicated to the study of a nonlinear SPDE on a bounded domain in Rd, with zero initial conditions and Dirichlet boundary, driven by an α-stable Lévy noise Z with α∈(0,2), α≠1, and possibly nonsymmetric tails. To give a meaning to the concept of solution, we develop a theory of stochastic integration with respect to this noise. The idea is to first solve the equation with “truncated” noise (obtained by removing from Z the jumps which exceed a fixed value K), yielding a solution uK, and then show that the solutions uL,L>K coincide on the event t≤τK, for some stopping times τK c

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13

Santos, P. V., F. A. da Costa, and J. M. de Araújo. "Mean-field solution of the Blume–Capel model under a random crystal field." Physics Letters A 379, no. 22-23 (2015): 1397–401. http://dx.doi.org/10.1016/j.physleta.2015.03.029.

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14

Hedegård, Per, and Anders Smith. "Solution of the Boltzmann equation in a random magnetic field." Physical Review B 51, no. 16 (1995): 10869–74. http://dx.doi.org/10.1103/physrevb.51.10869.

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15

Alonso, J. J., and J. Marro. "Mean-field solution of a nonequilibrium random-exchange Ising-model system." Physical Review B 45, no. 18 (1992): 10408–18. http://dx.doi.org/10.1103/physrevb.45.10408.

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16

Xing, B., and H. Umezawa. "Mean-field solution for random mixturesAxB1−xof an Ising site model." Physical Review B 46, no. 22 (1992): 14563–65. http://dx.doi.org/10.1103/physrevb.46.14563.

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17

da Silva, Claudio Roberto Ávila, Hilbeth Parente Azikri de Deus, Antonio Kozlik, and Oscar S. Garcia. "Application of the Method of Galerkin to Non Linear Problem Stochastic Heat Conduction One-Dimensional." Applied Mechanics and Materials 751 (April 2015): 325–30. http://dx.doi.org/10.4028/www.scientific.net/amm.751.325.

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The Galerkin method is applied in the non-linear stochastic diffusion problem. The uncertainty is present in the coefficients of diffusion equation. The uncertainty is modeled by random variables. The chaos polynomials is used to approximate the stochastic behavior of the problem. The approximate solutions obtained through Galerkin method are compared with Monte Carlo simulation in terms of the statistical moments of random variables generated by the random field solution.

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18

Ma, Jing-Ze, and Bing Zhang. "Relativistic oblique shocks with ordered or random magnetic fields: tangential field governs." Monthly Notices of the Royal Astronomical Society 511, no. 1 (2022): 925–37. http://dx.doi.org/10.1093/mnras/stac060.

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ABSTRACT Relativistic magnetohydrodynamic shocks are efficient particle accelerators, often invoked in the models of gamma-ray bursts (GRBs) and shock-powered fast radio bursts (FRBs). Most theoretical studies assume a perpendicular shock with an ordered magnetic field perpendicular to the shock normal. However, the degree of magnetization σ and the magnetic field geometry in shock-powered GRB/FRB scenarios are still poorly constrained by observations. Analogous to the magnetization σ associated with the total field strength, we define a tangential magnetization σ⊥ associated with the tangenti

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19

Martinelli, Sheri L. "Simulation of Propagating Acoustic Wavefronts with Random Sound Speed." Communications in Computational Physics 16, no. 4 (2014): 1081–101. http://dx.doi.org/10.4208/cicp.250913.080414a.

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AbstractA method for simulating acoustic wavefronts propagating under random sound speed conditions is presented. The approach applies a level set method to solve the Eikonal equation of high frequency acoustics for surfaces of constant phase, instead of tracing rays. The Lagrangian nature often makes full-field ray solutions difficult to reconstruct. The level set method captures multiple-valued solutions on a fixed grid. It is straightforward to represent other sources of uncertainty in the input data using this model, which has an advantage over Monte Carlo approaches in that it yields an e

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20

Huang, Tai, Kuangang Fan, Wen Sun, Weichao Li, and Haoqi Guo. "Potential-Field-RRT: A Path-Planning Algorithm for UAVs Based on Potential-Field-Oriented Greedy Strategy to Extend Random Tree." Drones 7, no. 5 (2023): 331. http://dx.doi.org/10.3390/drones7050331.

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This paper proposes a random tree algorithm based on a potential field oriented greedy strategy for the path planning of unmanned aerial vehicles (UAVs). Potential-field-RRT (PF-RRT) discards the defect of traditional artificial potential field (APF) algorithms that are prone to fall into local errors, and introduces potential fields as an aid to the expansion process of random trees. It reasonably triggers a greedy strategy based on the principle of field strength descending gradient optimization, accelerating the process of random tree expansion to a better region and reducing path search ti

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21

Sumedha and Mustansir Barma. "Solution of the random field XY magnet on a fully connected graph." Journal of Physics A: Mathematical and Theoretical 55, no. 9 (2022): 095001. http://dx.doi.org/10.1088/1751-8121/ac4b8b.

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Abstract We use large deviation theory to obtain the free energy of the XY model on a fully connected graph on each site of which there is a randomly oriented field of magnitude h. The phase diagram is obtained for two symmetric distributions of the random orientations: (a) a uniform distribution and (b) a distribution with cubic symmetry. In both cases, the disorder–averaged ordered state reflects the symmetry of the underlying distribution. The phase boundary has a multicritical point (MCP) which separates a locus of continuous transitions (for small values of h) from a locus of first order

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22

Serva, M., G. Paladin, and J. Raboanary. "Mean-field solution of the random Ising model on the dual lattice." Physical Review E 53, no. 1 (1996): R9—R12. http://dx.doi.org/10.1103/physreve.53.r9.

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23

Pasaric, Zoran. "The expectation of solution of random continuity equation with Gaussian velocity field." Glasnik Matematicki 38, no. 2 (2003): 359–76. http://dx.doi.org/10.3336/gm.38.2.13.

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24

Shadare, A. E., M. N. O. Sadiku, and S. M. Musa. "Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions." Advanced Electromagnetics 8, no. 5 (2019): 29–36. http://dx.doi.org/10.7716/aem.v8i5.1255.

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The advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods could be time-consuming because they calculate potential one point at a time. Thus, Markov Chain Monte Carlo (MCMC) is generally preferred to other Monte Carlo methods when considering whole-field computation. In this paper, MCMC has been applied to solve Poisson’s equation in homogeneous and inhomoge

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25

He, L., Z. Wu, Y. Zhang, and Z. Hu. "SEMANTIC SEGMENTATION OF REMOTE SENSING IMAGERY USING OBJECT-BASED MARKOV RANDOM FIELD BASED ON HIERARCHICAL SEGMENTATION TREE WITH AUXILIARY LABELS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLIII-B3-2020 (August 21, 2020): 75–81. http://dx.doi.org/10.5194/isprs-archives-xliii-b3-2020-75-2020.

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Abstract. In the remote sensing imagery, spectral and texture features are always complex due to different landscapes, which leads to misclassifications in the results of semantic segmentation. The object-based Markov random field provides an effective solution to this problem. However, the state-of-the-art object-based Markov random field still needs to be improved. In this paper, an object-based Markov Random Field model based on hierarchical segmentation tree with auxiliary labels is proposed. A remote sensing imagery is first segmented and the object-based hierarchical segmentation tree is

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26

R. Shakir, Ressol. "Studying the Effect of Scale of Fluctuation on the Flow Through an Earth Dam Using Stochastic Finite Element." University of Thi-Qar Journal for Engineering Sciences 2, no. 4 (2011): 116–30. http://dx.doi.org/10.31663/utjes.v2i4.164.

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Estimation of quantity of flow through earth dams by using finite elements method mainly depends on the magnitudes of permeability for the earth dam. The permeability of soil medium may be included in the solution as constant permeability or non homogeneous, anisotropic or may be distributed as random field. Simulation of properties of soil by using random fields’ generators has great interest nowadays. This paper includes studying of the effect of anisotropy of scale of fluctuation of the permeability through the stochastic finite elements analysis for case of flow through earth dam. Permeabi

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27

Slobodian, S. Ya. "The normal limit distribution of the normalized number of false solutions of a one system of nonlinear random equations over the field GF(2)." Carpathian Mathematical Publications 6, no. 1 (2014): 149–60. http://dx.doi.org/10.15330/cmp.6.1.149-160.

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The theorem on a normal limit distribution of the normalized number of false solutions of a beforehand consistent system of nonlinear random equations over the field GF(2) is proved. The results with the additional condition on the number of nonzero components both false solutions and true solution of the solutions are obtained.

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28

Igarashi, Harukazu. "A solution for combinational optimization problems using a two-layer random field model-mean-field approximation." Systems and Computers in Japan 25, no. 8 (1994): 61–71. http://dx.doi.org/10.1002/scj.4690250806.

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29

Chitose, Makoto, Hiroki Suzuki, and Toshinori Kouchi. "Energy conservation uncertainly due to the use of an implicit time integration method clarified by a multiplexed TGV inviscid flow." Journal of Physics: Conference Series 2701, no. 1 (2024): 012059. http://dx.doi.org/10.1088/1742-6596/2701/1/012059.

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Abstract This study attempts to elucidate the conservation errors induced by the implicit time integration method within a multiscale flow. Using the multiplexed Taylor analytical solution as the initial field, three distinct multiscale turbulence fields were formulated, each characterised by different wavenumber attributes. A two-dimensional inviscid flow field, replicated in a computational domain with a side of 2π and subject to periodic boundary conditions, was used to illuminate kinetic energy conservation errors. The implicit time integration method - specifically the second-order accura

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30

Dorlas, T. C., and J. R. Wedagedera. "Rigorous solution of a mean field spin glass model." Journal of Applied Mathematics and Stochastic Analysis 13, no. 2 (2000): 147–60. http://dx.doi.org/10.1155/s1048953300000162.

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A separable spin glass model whose exchange integral takes the form Jij=J(ξi1ξj2+ξi2ξj1) which was solved by van Hemmen et al. [12] using large deviation theory [14] is rigorously treated. The almost sure convergence criteria associated with the cumulant generating function C(t) with respect to the quenched random variables ξ is carefully investigated, and it is proved that the related excluded null set 𝒩 is independent of t. The free energy and hence the other thermodynamic quantities are rederived using Varadhan's Large Deviation Theorem. A simulation is also presented for the entropy when ξ

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31

Jadaliha, Mahdi, Jinho Jeong, Yunfei Xu, Jongeun Choi, and Junghoon Kim. "Fully Bayesian Prediction Algorithms for Mobile Robotic Sensors under Uncertain Localization Using Gaussian Markov Random Fields." Sensors 18, no. 9 (2018): 2866. http://dx.doi.org/10.3390/s18092866.

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In this paper, we present algorithms for predicting a spatio-temporal random field measured by mobile robotic sensors under uncertainties in localization and measurements. The spatio-temporal field of interest is modeled by a sum of a time-varying mean function and a Gaussian Markov random field (GMRF) with unknown hyperparameters. We first derive the exact Bayesian solution to the problem of computing the predictive inference of the random field, taking into account observations, uncertain hyperparameters, measurement noise, and uncertain localization in a fully Bayesian point of view. We sho

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32

Lazarian, A. "Statistical Method for Astrophysical Turbulence Investigation." Symposium - International Astronomical Union 157 (1993): 427–28. http://dx.doi.org/10.1017/s007418090017456x.

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Present-day galactic dynamo theories widely use a concept of the ISM turbulence. In the present paper a statistical method of MHD turbulence study is discussed. The method is based on the solution of the inverse problem for the observational data. It is shown that in many important cases the inverse problem has a unique analytical solution. Examples, including the study of a random density field and a random magnetic field, are discussed.

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33

HOANG, VIET HA, and CHRISTOPH SCHWAB. "N-TERM WIENER CHAOS APPROXIMATION RATES FOR ELLIPTIC PDEs WITH LOGNORMAL GAUSSIAN RANDOM INPUTS." Mathematical Models and Methods in Applied Sciences 24, no. 04 (2014): 797–826. http://dx.doi.org/10.1142/s0218202513500681.

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We consider diffusion in a random medium modeled as diffusion equation with lognormal Gaussian diffusion coefficient. Sufficient conditions on the log permeability are provided in order for a weak solution to exist in certain Bochner–Lebesgue spaces with respect to a Gaussian measure. The stochastic problem is reformulated as an equivalent deterministic parametric problem on ℝℕ. It is shown that the weak solution can be represented as Wiener–Itô Polynomial Chaos series of Hermite Polynomials of a countable number of i.i.d standard Gaussian random variables taking values in ℝ1. We establish suf

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34

Forgács, G., W. F. Wolff, and A. Süt. "Exact solution of a two-dimensional Ising model in a random magnetic field." Physical Review B 31, no. 9 (1985): 6089–91. http://dx.doi.org/10.1103/physrevb.31.6089.

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35

Zasenko, V. I., A. G. Zagorodny, and J. Weiland. "Permittivity of Plasma in Random Fields of Moderate Intensity." Ukrainian Journal of Physics 56, no. 7 (2022): 654. http://dx.doi.org/10.15407/ujpe56.7.654.

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The permittivity of plasma in the electric field of random waves of moderate intensity is given in terms of the particle transition probability between two points of the phase space. The transition probability was found as an approximate solution of the Fokker–Planck equation. Validity of this analytical approximation was verified by the direct simulation of the particle diffusion in a field of random waves.

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36

NOVOTNY, M. A., and A. KOLAKOWSKA. "MIXING DIFFERENT RANDOM DEPOSITIONS IN NONEQUILIBRIUM SURFACE GROWTH MODELS." International Journal of Modern Physics C 20, no. 09 (2009): 1377–85. http://dx.doi.org/10.1142/s0129183109014448.

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An exact solution is presented for mixing two or more different types of Random Deposition (RD) nonequilibrium surface growth processes. The depositions may be made in a sequential mode, or in a random mode by first randomly choosing the lattice site for deposition. The results hold in all dimensions d. Simulations are presented in d = 1 for comparison. Furthermore, a mean-field type of approach to mixing RD with other surface growth processes is tested against the exact solution.

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37

Richter, O., and B. Diekkrüger. "Translating environmental xenobiotic fate models across scales." Hydrology and Earth System Sciences 1, no. 4 (1997): 895–904. http://dx.doi.org/10.5194/hess-1-895-1997.

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Abstract. The classical models developed for degradation and transport of xenobiotics have been derived with the assumption of homogeneous environments. Unfortunately, deterministic models function well in the laboratory under homogeneous conditions but such homogeneous conditions often do not prevail in the field. A possible solution is the incorporation of the statistical variation of soil parameters into deterministic process models. This demands the development of stochastic models of spatial variability. To this end, spatial soil parameter fields are conceived as the realisation of a rand

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38

NIEMIEC, M., W. OLCHAWA, L. SCHIMANSKY-GEIER, and J. ŁUCZKA. "KINETICS OF CRYSTAL GROWTH LIMITED BY RANDOM VELOCITY FIELDS." International Journal of Bifurcation and Chaos 18, no. 09 (2008): 2673–79. http://dx.doi.org/10.1142/s0218127408021889.

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A spherical growth process controlled by velocity fluctuations of particles of a saturated solution is investigated. Velocity fluctuations are modeled by a Gaussian random field. The interface evolution is determined by a Langevin-type equation with a multiplicative random field, which in the case of the quasi-homogeneous random Gaussian field is equivalent to Fokker–Planck dynamics. We analyze numerically the Fokker–Planck equation and compare growth kinetics in the case of noisy (i.e. space-independent) fluctuations. It is shown that for a large class of spatially correlated velocity fluctua

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Lugovy, M. I., D. G. Verbylo, and M. P. Brodnikovskyy. "Modelling of shear stress field in glide plane in substitutional solid solutions." Uspihi materialoznavstva 2021, no. 3 (2021): 24–37. http://dx.doi.org/10.15407/materials2021.03.024.

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The formation of stochastic shear stress field in the glide plane in the substitutional solid solution was investigated by computer simulation. If the atoms in the crystal lattice nodes of the substitutional solid solution are considered as a kind of point defects in the virtual solvent medium, the shear stress distribution in the glide plane can be calculated based on the interaction of edge dislocation and such defects. For concentrated solid solutions, the shear stress will be a normally distributed random value with zero mathematical expectation. The standard deviation of this distribution

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Forgacs, G., W. F. Wolff, and A. Suto. "Exact solution of a two-dimensional Ising model in a correlated random magnetic field." Journal of Physics A: Mathematical and General 19, no. 10 (1986): 1899–911. http://dx.doi.org/10.1088/0305-4470/19/10/031.

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41

Tong, Junhua, Songtao Li, Chao Chen, et al. "Flexible Random Laser Using Silver Nanoflowers." Polymers 11, no. 4 (2019): 619. http://dx.doi.org/10.3390/polym11040619.

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A random laser was achieved in a polymer membrane with silver nanoflowers on a flexible substrate. The strong confinement of the polymer waveguide and the localized field enhancement of silver nanoflowers were essential for the low-threshold random lasing action. The lasing wavelength can be tuned by bending the flexible substrate. The solution phase synthesis of the silver nanoflowers enables easy realization of this type of random lasers. The flexible and high-efficiency random lasers provide favorable factors for the development of imaging and sensing devices.

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42

Ostoja-Starzewski, Martin. "Plastic Flow of Random Media: Micromechanics, Markov Property and Slip-Lines." Applied Mechanics Reviews 45, no. 3S (1992): S75—S81. http://dx.doi.org/10.1115/1.3121394.

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The classical method of slip-lines (characteristics) of planar flow of perfectly-plastic media is generalized to a stochastic setting. The media are charaterized by space-homogeneous statistics of the yield limit k, whose derivation is outlined on the basis of micromechanics. The field equations of the random continuum approximation lead to a stochastic hyperbolic system. This system, when stated in a finite difference form, displays a Markov property for the forward evolution. On that basis, two methods of solution of boundary value problems - an exact one and a mean-field one - are outlined

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Ostoja-Starzewski, M. "Micromechanics as a Basis of Stochastic Finite Elements and Differences: An Overview." Applied Mechanics Reviews 46, no. 11S (1993): S136—S147. http://dx.doi.org/10.1115/1.3122629.

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A generalization of conventional deterministic finite element and difference methods to deal with spatial material fluctuations hinges on the problem of determination of stochastic constitutive laws. This problem is analyzed here through a paradigm of micromechanics of elastic polycrystals and matrix-inclusion composites. Passage to a sought-for random meso-continuum is based on a scale dependent window playing the role of a Representative Volume Element (RVE). It turns out that the microstructure cannot be uniquely approximated by a random field of stiffness with continuous realizations, but,

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44

Zangl, Hubert, Lisa-Marie Faller, and Wolfgang Granig. "Optimal design of angular position sensors." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 5 (2017): 1372–85. http://dx.doi.org/10.1108/compel-02-2017-0099.

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Purpose This paper aims to investigate the optimal placement and/or orientation of individual sensor elements within integrated angular position sensors, in particular magnetic sensors based on the Hall effect or magnetoresistive effects under consideration of random deviations (variations in the production process, environmental influences, noise) and correlations of these influences. Design/methodology/approach The authors utilize methods from optimal design of experiments to consider random deviations in a system-level model. In this sensor model, they include spatial dependencies of random

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Finkelshtein, Dmitri, Yuri Kondratiev, Stanislav Molchanov, and Pasha Tkachov. "Global stability in a nonlocal reaction-diffusion equation." Stochastics and Dynamics 18, no. 05 (2018): 1850037. http://dx.doi.org/10.1142/s0219493718500375.

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We study stability of stationary solutions for a class of nonlocal semilinear parabolic equations. To this end, we prove the Feynman–Kac formula for a Lévy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the zero solution, and use them to the study of the spatial logistic equation arising in population ecology. For this equation, we find conditions which imply that its positive stationary solution is asymptotically stable. We consider also the case when the initial condition is given by a random field.

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DORLAS, T. C., and J. R. WEDAGEDERA. "LARGE DEVIATIONS AND THE RANDOM ENERGY MODEL." International Journal of Modern Physics B 15, no. 01 (2001): 1–15. http://dx.doi.org/10.1142/s0217979201002552.

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We present a simple proof of the formula for the free energy of the random energy model using a large deviation property which holds almost surely with respect to the randomness. This proof is extended to the case with external magnetic field leading to the solution of a model with higher-order ferromagnetic term. It is shown that this model is useful for Sourlas' application to error-correcting codes as was already pointed out in a recent letter by the authors.

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Boichenko, Viktoriia, Nataliya Shchestyuk, and Anastasiia Florenko. "Interpolation problems for random fields on Sierpinski’s carpet." Mohyla Mathematical Journal 6 (April 18, 2024): 28–34. http://dx.doi.org/10.18523/2617-70806202328-34.

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The prediction of stochastic processes and the estimation of random fields of different natures is becoming an increasingly common field of research among scientists of various specialties. However, an analysis of papers across different estimating problems shows that a dynamic approach over an iterative and recursive interpolation of random fields on fractal is still an open area of investigation. There are many papers related to the interpolation problems of stationary sequences, estimation of random fields, even on the perforated planes, but all of this still provides a place for an investi

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Cordero-Grande, Lucilio, Gonzalo Vegas-Sanchez-Ferrero, Pablo Casaseca, et al. "Unsupervised 4D myocardium segmentation with a Markov Random Field based deformable model." Medical Image Analysis 15 (February 25, 2011): 283–301. https://doi.org/10.5281/zenodo.14791347.

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A stochastic deformable model is proposed for the segmentation of the myocardium in Magnetic Resonance Imaging. The segmentation is posed as a probabilistic optimization problem in which the optimal time-dependent surface is obtained for the myocardium of the heart in a discrete space of locations built upon simple geometric assumptions. For this purpose, first, the left ventricle is detected by a set of image analysis tools gathered from the literature. Then, the segmentation solution is obtained by the Maximization of the Posterior Marginals for the myocardium location in a Markov Random Fie

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Jerez-Hanckes, Carlos, Christoph Schwab, and Jakob Zech. "Electromagnetic wave scattering by random surfaces: Shape holomorphy." Mathematical Models and Methods in Applied Sciences 27, no. 12 (2017): 2229–59. http://dx.doi.org/10.1142/s0218202517500439.

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For time-harmonic electromagnetic waves scattered by either perfectly conducting or dielectric bounded obstacles, we show that the fields depend holomorphically on the shape of the scatterer. In the presence of random geometrical perturbations, our results imply strong measurability of the fields, in weighted spaces in the exterior of the scatterer. These findings are key to prove dimension-independent convergence rates of sparse approximation techniques of polynomial chaos type for forward and inverse computational uncertainty quantification. Also, our shape-holomorphy results imply parsimoni

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Ding, Fang, Aiguo Wang, and Qianbin Zhang. "Lane Line Identification and Research Based on Markov Random Field." World Electric Vehicle Journal 13, no. 6 (2022): 106. http://dx.doi.org/10.3390/wevj13060106.

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In view of the poor robustness and low accuracy in lane line identification based on digital image processing, this paper proposes a Markov random field intelligent algorithm based on machine learning to identify lane lines. The complete lane line identification steps are as follows: First, high-quality traffic scenario images are created by means of image preprocessing, which includes image graying, grayscale transformation, and the extraction of regions of interest (ROIs). Then, the images are modeled according to Markov random field theory, and model reasoning is performed based on the bina

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