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Journal articles on the topic 'Stochastic analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

PE and P. Malliavin. "Stochastic Analysis." Journal of the American Statistical Association 93, no. 441 (1998): 411. http://dx.doi.org/10.2307/2669659.

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2

Hu, Peng, та Chengming Huang. "The StochasticΘ-Method for Nonlinear Stochastic Volterra Integro-Differential Equations". Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/583930.

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The stochasticΘ-method is extended to solve nonlinear stochastic Volterra integro-differential equations. The mean-square convergence and asymptotic stability of the method are studied. First, we prove that the stochasticΘ-method is convergent of order1/2in mean-square sense for such equations. Then, a sufficient condition for mean-square exponential stability of the true solution is given. Under this condition, it is shown that the stochasticΘ-method is mean-square asymptotically stable for every stepsize if1/2≤θ≤1and when0≤θ<1/2, the stochasticΘ-method is mean-square asymptotically stable

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3

Markus, L., and A. Weerasinghe. "Stochastic oscillators." Journal of Differential Equations 71, no. 2 (1988): 288–314. http://dx.doi.org/10.1016/0022-0396(88)90029-0.

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4

Sankar, T. S., S. A. Ramu, and R. Ganesan. "Stochastic Finite Element Analysis for High Speed Rotors." Journal of Vibration and Acoustics 115, no. 1 (1993): 59–64. http://dx.doi.org/10.1115/1.2930315.

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The general problem of the dynamic response of highspeed rotors is considered in which certain system parameters may have a spatial stochastic variation. In particular the elastic modulus and mass density of a rotating shaft are described through one dimensional stochastic field functions so that the imperfections in manufacture and measurement can be accounted for. The stochastic finite element method is developed so that the variability of the response of the rotor can be interpreted in terms of the variation of the material property. As an illustration the whirl speed analysis is performed

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5

Zhao, Wenqiang, and Yangrong Li. "Existence of Random Attractors for ap-Laplacian-Type Equation with Additive Noise." Abstract and Applied Analysis 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/616451.

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We first establish the existence and uniqueness of a solution for a stochasticp-Laplacian-type equation with additive white noise and show that the unique solution generates a stochastic dynamical system. By using the Dirichlet forms of Laplacian and an approximation procedure, the nonlinear obstacle, arising from the additive noise is overcome when we make energy estimate. Then, we obtain a random attractor for this stochastic dynamical system. Finally, under a restrictive assumption on the monotonicity coefficient, we find that the random attractor consists of a single point, and therefore t

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6

Hengki, Tamando Sihotang, Efendi Syahril, Zarlis Muhammad, and Mawengkang Herman. "Data driven approach for stochastic data envelopment analysis." Bulletin of Electrical Engineering and Informatics 11, no. 3 (2022): 1497~1504. https://doi.org/10.11591/eei.v11i3.3660.

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Decision making based on data driven deals with a large amount of data will evaluate the process's effectiveness. Evaluate effectiveness in this paper is measure of performance efficiency of data envelopment analysis (DEA) method in this study is the approach with uncertainty problems. This study proposed a new method called the robust stochastic DEA (RSDEA) to approach performance efficiency in tackling uncertainty problems (i.e., stochastic and robust optimization). The RSDEA method develops to combine the stochastics DEA (SDEA) formulation method and Robust Optimization. The numerical e

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7

IMKELLER, PETER, and ADAM HUGH MONAHAN. "CONCEPTUAL STOCHASTIC CLIMATE MODELS." Stochastics and Dynamics 02, no. 03 (2002): 311–26. http://dx.doi.org/10.1142/s0219493702000443.

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From July 9 to 11, 2001, 50 researchers from the fields of climate dynamics and stochastic analysis met in Chorin, Germany, to discuss the idea of stochastic models of climate. The present issue of Stochastics and Dynamics collects several papers from this meeting. In this introduction to the volume, the idea of simple conceptual stochastic climate models is introduced amd recent results in the mathematically rigorous development and analysis of such models are reviewed. As well, a brief overview of the application of ideas from stochastic dynamics to simple models of the climate system is giv

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8

Ocone, Daniel. "Stochastic calculus of variations for stochastic partial differential equations." Journal of Functional Analysis 79, no. 2 (1988): 288–331. http://dx.doi.org/10.1016/0022-1236(88)90015-8.

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9

Sihotang, Hengki Tamando, Syahril Efendi, Muhammad Zarlis, and Herman Mawengkang. "Data driven approach for stochastic data envelopment analysis." Bulletin of Electrical Engineering and Informatics 11, no. 3 (2022): 1497–504. http://dx.doi.org/10.11591/eei.v11i3.3660.

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Decision making based on data driven deals with a large amount of data will evaluate the process's effectiveness. Evaluate effectiveness in this paper is measure of performance efficiency of data envelopment analysis (DEA) method in this study is the approach with uncertainty problems. This study proposed a new method called the robust stochastic DEA (RSDEA) to approach performance efficiency in tackling uncertainty problems (i.e., stochastic and robust optimization). The RSDEA method develops to combine the stochastics DEA (SDEA) formulation method and Robust Optimization. The numerical examp

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10

OGURA, Yukio. "Stochastic Fuzzy Analysis." Journal of Japan Society for Fuzzy Theory and Systems 10, no. 6 (1998): 1012–19. http://dx.doi.org/10.3156/jfuzzy.10.6_1012.

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11

Schmidt, Peter. "Stochastic Frontier Analysis." Economic Journal 112, no. 477 (2002): F156—F158. http://dx.doi.org/10.1111/1468-0297.0688l.

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12

Irving, A. D. "Stochastic sensitivity analysis." Applied Mathematical Modelling 16, no. 1 (1992): 3–15. http://dx.doi.org/10.1016/0307-904x(92)90110-o.

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13

Hayre, Lakhbir S., Charles Huang, and Vincent Pica. "Stochastic Horizon Analysis." Journal of Fixed Income 3, no. 1 (1993): 48–53. http://dx.doi.org/10.3905/jfi.1993.408074.

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14

Eschenbach, Ted G., and Robert J. Gimpel. "Stochastic Sensitivity Analysis." Engineering Economist 35, no. 4 (1990): 305–21. http://dx.doi.org/10.1080/00137919008903024.

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15

Zhang, Xicheng. "Stochastic Volterra equations in Banach spaces and stochastic partial differential equation." Journal of Functional Analysis 258, no. 4 (2010): 1361–425. http://dx.doi.org/10.1016/j.jfa.2009.11.006.

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16

Zhou, Peiyuan, and Jinling Wang. "Stochastic Ionosphere Models for Precise GNSS Positioning: Sensitivity Analysis." Journal of Global Positioning Systems 12, no. 1 (2013): 53–60. http://dx.doi.org/10.5081/jgps.12.1.53.

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17

Zhao, Yihan, Yuanpei Xia, and Zhichun Yang. "Asymptotic behavior of stochastic three-species predator-prey systems with white and Levy noise." Electronic Journal of Differential Equations 2020, no. 01-132 (2020): 71. http://dx.doi.org/10.58997/ejde.2020.71.

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In this article, we propose a three-species prey-predator system with Holling II functional response and stochastic perturbations involving white noise and Levy noise. Firstly, we study the existence and uniqueness of a global positive solution and stochastic ultimate boundedness. Then, we obtain sufficient conditions for stability, extinction, strongly persistence in the mean and stochastic permanence in the sense of probability for the stochastic system. The results show that both white noise and Levy noise may change the asymptotic properties of the population system. Finally, some examples

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18

Wang, Peiguang, and Yan Xu. "Averaging Method for Neutral Stochastic Delay Differential Equations Driven by Fractional Brownian Motion." Journal of Function Spaces 2020 (May 29, 2020): 1–7. http://dx.doi.org/10.1155/2020/5212690.

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In this paper, we investigate the stochastic averaging method for neutral stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H∈1/2,1. By using the linear operator theory and the pathwise approach, we show that the solutions of neutral stochastic delay differential equations converge to the solutions of the corresponding averaged stochastic delay differential equations. At last, an example is provided to illustrate the applications of the proposed results.

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19

Duan, Pengju. "SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions." Journal of Function Spaces 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/5916132.

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The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by constructing Cauchy sequence and fixed point theorem. Moreover, we give a probabilistic solution of stochastic partial differential integral equations by means of the solution of backward stochastic differential equations. Finally, we give an example to illustrate.

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20

Albeverio, S., Y. G. Kondratiev, and M. Rockner. "Dirichlet Operators via Stochastic Analysis." Journal of Functional Analysis 128, no. 1 (1995): 102–38. http://dx.doi.org/10.1006/jfan.1995.1025.

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21

Chen, Ye-Jun, and Hui-Sheng Ding. "Pseudo almost periodicity for stochastic differential equations in infinite dimensions." Electronic Journal of Differential Equations 2023, no. 01-37 (2023): 34. http://dx.doi.org/10.58997/ejde.2023.34.

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In this article, we introduce the concept of p-mean θ-pseudo almost periodic stochastic processes, which is slightly weaker than p-mean pseudo almost periodic stochastic processes. Using the operator semigroup theory and stochastic analysis theory, we obtain the existence and uniqueness of square-mean θ-pseudo almost periodic mild solutions for a semilinear stochastic differential equation in infinite dimensions. Moreover, we prove that the obtained solution is also pseudo almost periodic in path distribution. It is noteworthy that the ergodic part of the obtained solution is not only ergodic

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22

Lu, Jin-Biao, Zhi-Jiang Liu, Dmitry Tulenty, Liudmila Tsvetkova, and Sebastian Kot. "Implementation of Stochastic Analysis in Corporate Decision-Making Models." Mathematics 9, no. 9 (2021): 1041. http://dx.doi.org/10.3390/math9091041.

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The stochastic approach as a method for modeling factor systems of interrelationships of economic activity aspects allows minimizing managerial errors against the background of company growth and expansion of operating activities. The purpose of this study is to form a decision-making model to ensure the financial competitiveness of enterprises in the context of stochastic analysis. This study demonstrates stochastic analysis implementation in companies of the 2nd and 3rd degrees of internationalization based on multiple regression and factorial analysis of variance. The practical basis of the

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23

Fukuizumi, Reika, and Leo Hahn. "Stochastic Schrödinger-Lohe model." Journal of Functional Analysis 281, no. 10 (2021): 109224. http://dx.doi.org/10.1016/j.jfa.2021.109224.

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24

Kloeden, Peter E., and Thomas Lorenz. "Stochastic morphological evolution equations." Journal of Differential Equations 251, no. 10 (2011): 2950–79. http://dx.doi.org/10.1016/j.jde.2011.03.013.

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25

Ben Makhlouf, Abdellatif, Lassaad Mchiri, and Mohamed Rhaima. "Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods." Journal of Function Spaces 2021 (April 21, 2021): 1–7. http://dx.doi.org/10.1155/2021/5544847.

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The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples

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26

Xiao, Qingkun, and Hongjun Gao. "Stochastic attractor bifurcation for the two-dimensional Swift-Hohenberg equation with multiplicative noise." Electronic Journal of Differential Equations 2023, no. 01-37 (2023): 20. http://dx.doi.org/10.58997/ejde.2023.20.

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This article concerns the dynamical transitions of the stochastic Swift-Hohenberg equation with multiplicative noise on a two-dimensional domain (-L,L) times (-L, L). With α and L regarded as parameters, we show that the approximate reduced system corresponding to the invariant manifold undergoes a stochastic pitchfork bifurcation near the critical points, and the impact of noise on stochastic bifurcation of the Swift-Hohenberg equation. We find the approximation representation of the manifold and the corresponding reduced systems for stochastic Swift-Hohenberg equation when L2 and √2L1 are cl

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27

Li, Fei, Xinzhu Meng, and Yujun Cui. "Nonlinear stochastic analysis for a stochastic SIS epidemic model." Journal of Nonlinear Sciences and Applications 10, no. 09 (2017): 5116–24. http://dx.doi.org/10.22436/jnsa.010.09.47.

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28

Huang, Zhehao, and Zhengrong Liu. "Stochastic traveling wave solution to stochastic generalized KPP equation." Nonlinear Differential Equations and Applications NoDEA 22, no. 1 (2014): 143–73. http://dx.doi.org/10.1007/s00030-014-0279-9.

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29

Meng, Qingxin, and Peng Shi. "Stochastic optimal control for backward stochastic partial differential systems." Journal of Mathematical Analysis and Applications 402, no. 2 (2013): 758–71. http://dx.doi.org/10.1016/j.jmaa.2013.01.053.

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30

Iwanik, Anzelm, and Ray Shiflett. "The root problem for stochastic and doubly stochastic operators." Journal of Mathematical Analysis and Applications 113, no. 1 (1986): 93–112. http://dx.doi.org/10.1016/0022-247x(86)90335-5.

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31

Larsson, Martin, and Johannes Ruf. "Stochastic exponentials and logarithms on stochastic intervals — A survey." Journal of Mathematical Analysis and Applications 476, no. 1 (2019): 2–12. http://dx.doi.org/10.1016/j.jmaa.2018.11.040.

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32

Brzeźniak, Zdzisław, Wei Liu, and Jiahui Zhu. "The stochastic Strichartz estimates and stochastic nonlinear Schrödinger equations driven by Lévy noise." Journal of Functional Analysis 281, no. 4 (2021): 109021. http://dx.doi.org/10.1016/j.jfa.2021.109021.

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33

Durastante, Fabio, and Beatrice Meini. "Stochastic \({p}\)th Root Approximation of a Stochastic Matrix: A Riemannian Optimization Approach." SIAM Journal on Matrix Analysis and Applications 45, no. 2 (2024): 875–904. http://dx.doi.org/10.1137/23m1589463.

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34

Albeverio, Sergio, Raphael Høegh-Krohn, and Helge Holden. "Stochastic multiplicative measures, generalized Markov semigroups, and group-valued stochastic processes and fields." Journal of Functional Analysis 78, no. 1 (1988): 154–84. http://dx.doi.org/10.1016/0022-1236(88)90137-1.

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35

Pilipović, Stevan, and Dora Seleši. "On the Generalized Stochastic Dirichlet Problem—Part I: The Stochastic Weak Maximum Principle." Potential Analysis 32, no. 4 (2009): 363–87. http://dx.doi.org/10.1007/s11118-009-9155-3.

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36

Lu, Chun. "Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate." Journal of Function Spaces 2022 (January 17, 2022): 1–8. http://dx.doi.org/10.1155/2022/5574983.

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The article researches a stochastic hepatitis B epidemic model with saturated incidence rate, which is perturbed by both white noise and colored noise. Firstly, we obtain a significant criterion R 0 S which relies on environmental noises. By means of Lyapunov function approach, we show that there is a stationary distribution if R 0 S > 1 . Its condition implies that when white noise is small, in the stochastic model, there exists a stochastic positive equilibrium state without changing the basic properties of its corresponding deterministic model. Secondly, we derive sufficient criteria for

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37

Lorist, Emiel, and Mark Veraar. "Singular stochastic integral operators." Analysis & PDE 14, no. 5 (2021): 1443–507. http://dx.doi.org/10.2140/apde.2021.14.1443.

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38

Carroll, Clodagh. "Supersymmetric quantum stochastic analysis." Irish Mathematical Society Bulletin 0066 (2010): 23–24. http://dx.doi.org/10.33232/bims.0066.23.24.

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39

Banker, Rajiv D. "Stochastic Data Envelopment Analysis." Data Envelopment Analysis Journal 5, no. 2 (2021): 281–309. http://dx.doi.org/10.1561/103.00000038.

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40

Varadhan, S. R. S. "Stochastic analysis and applications." Bulletin of the American Mathematical Society 40, no. 01 (2002): 89–98. http://dx.doi.org/10.1090/s0273-0979-02-00968-0.

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41

Durrett, Rick. "Book Review: Stochastic analysis." Bulletin of the American Mathematical Society 42, no. 02 (2005): 225–28. http://dx.doi.org/10.1090/s0273-0979-05-01042-6.

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42

Herbin, Erick, and Jacques Lévy-Véhel. "Stochastic 2-microlocal analysis." Stochastic Processes and their Applications 119, no. 7 (2009): 2277–311. http://dx.doi.org/10.1016/j.spa.2008.11.005.

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43

Driver, Bruce K. "Book Review: Stochastic analysis." Bulletin of the American Mathematical Society 35, no. 01 (1998): 99–105. http://dx.doi.org/10.1090/s0273-0979-98-00739-3.

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44

Jones, P. W. "Stochastic Modelling and Analysis." Technometrics 30, no. 3 (1988): 361. http://dx.doi.org/10.1080/00401706.1988.10488425.

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45

Essi, Nyong O., and M. M. Rao. "Real and Stochastic Analysis." Statistician 36, no. 4 (1987): 424. http://dx.doi.org/10.2307/2348854.

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46

Scheffer, C. L., and M. M. Rao. "Foundations of Stochastic Analysis." Journal of the American Statistical Association 80, no. 391 (1985): 788. http://dx.doi.org/10.2307/2288524.

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47

Lechtenberg, Christian. "Stochastic Frontier Analysis (SFA)." Controlling 23, no. 12 (2011): 682–83. http://dx.doi.org/10.15358/0935-0381-2011-12-682.

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48

Mangel, Marc. "Stochastic Analysis and Applications." Mathematical Biosciences 79, no. 2 (1986): 241–43. http://dx.doi.org/10.1016/0025-5564(86)90155-0.

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49

Ferschl, Franz. "Stochastic modelling and analysis." European Journal of Operational Research 28, no. 1 (1987): 113–14. http://dx.doi.org/10.1016/0377-2217(87)90185-8.

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50

Virtala, M. "Stochastic virtual population analysis." ICES Journal of Marine Science 55, no. 5 (1998): 892–904. http://dx.doi.org/10.1006/jmsc.1998.0368.

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