Stochastic averaging principles for multi-valued stochastic differential equations driven by poisson point Processes

被引：16

作者：

Guo, Rong ^{[1
]}

Pei, Bin ^{[2
,3
]}

机构：

[1] Taiyuan Univ Sci & Technol, Sch Appl Sci, Taiyuan, Shanxi, Peoples R China

[2] Xidian Univ, Sch Math & Stat, Xian 710071, Shaanxi, Peoples R China

[3] Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2018年 / 36卷 / 04期

关键词：

Multi-valued stochastic differential equations; Averaging principles; Poisson point processes; Maximal monotone operator; FRACTIONAL BROWNIAN-MOTION; OPTIMAL DIVIDEND PROBLEM; STRONG-CONVERGENCE RATE; DIFFUSION RISK PROCESS; DYNAMICAL-SYSTEMS; EVOLUTION-EQUATIONS; LEVY NOISE; SKOROHOD PROBLEM; MILD SOLUTIONS; TIME-SCALES;

D O I：

10.1080/07362994.2018.1461567

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this article is to investigate an averaging principle for multi-valued stochastic differential equations (MSDEs) driven by Poisson point processes. The solutions to MSDEs driven by Poisson point processes can be approximated by solutions to averaged MSDEs in the sense of both convergence in mean square and convergence in probability. Finally, an example is presented to illustrate the averaging principle.

引用

页码：751 / 766

页数：16

共 48 条

[21] Two-time-scales hyperbolic parabolic equations driven by Poisson random measures: Existence, uniqueness and averaging principles [J].

Pei, Bin ;

Xu, Yong ;

Wu, Jiang-Lun .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 447 (01) :243-268

[22] Mild solutions of local non-Lipschitz stochastic evolution equations with jumps [J].

Pei, Bin ;

Xu, Yong .

APPLIED MATHEMATICS LETTERS, 2016, 52 :80-86

[23]

Ren JG, 2011, PROG PROBAB, V65, P191

[24] On existence, uniqueness and convergence of multi-valued stochastic differential equations driven by continuous semimartingales [J].

Ren JiaGang ;

Wu Jing ;

Zhang Hua .

SCIENCE CHINA-MATHEMATICS, 2014, 57 (03) :589-607

[25] The optimal control problem associated with multi-valued stochastic differential equations with jumps [J].

Ren, Jiagang ;

Wu, Jing .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 86 :30-51

[26] Large Deviations for Multivalued Stochastic Differential Equations [J].

Ren, Jiagang ;

Xu, Siyan ;

Zhang, Xicheng .

JOURNAL OF THEORETICAL PROBABILITY, 2010, 23 (04) :1142-1156

[27] Exponential ergodicity of non-Lipschitz multivalued stochastic differential equations [J].

Ren, Jiagang ;

Wu, Jing ;

Zhang, Xicheng .

BULLETIN DES SCIENCES MATHEMATIQUES, 2010, 134 (04) :391-404

[28] A transfer principle for multivalued stochastic differential equations [J].

Ren, Jiagang ;

Xu, Siyan .

JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (09) :2780-2814

[29] Alternative Approach to the Optimality of the Threshold Strategy for Spectrally Negative Levy Processes [J].

Shen, Ying ;

Yin, Chuan-cun ;

Yuen, Kam Chuen .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2013, 29 (04) :705-716

[30]

Stoyanov I.M., 1974, UKRAINIAN MATH J, V26, P186

← 1 2 3 4 5 →