An Averaging Principle for Multivalued Stochastic Differential Equations

被引：18

作者：

Xu, Jie ^{[1
]}

Liu, Jicheng ^{[2
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2014年 / 32卷 / 06期

关键词：

Lipschitz coefficients; Brownian motion; Averaging principle; MSDEs;

D O I：

10.1080/07362994.2014.959594

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The averaging principle for multivalued stochastic differential equations (MSDEs) driven by Brownian motion with Brownian noise is investigated. An averaged MSDEs for the original MSDEs is proposed, and their solutions are quantitatively compared. Under suitable assumptions, it is shown that the solution of the MSDEs converges to that of the original MSDEs in the sense of mean square and also in probability. Two examples are presented to illustrate the averaging principle.

引用

页码：962 / 974

页数：13

共 17 条

[1]

[Anonymous], 1973, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert

[2] Multivalued Skorohod problem [J].

Cepa, E .

ANNALS OF PROBABILITY, 1998, 26 (02) :500-532

[3]

Ikeda I., 1989, STOCHASTIC DIFFERENT, P89

[4]

Khas'minskii R. Z., 1968, Kybernetika, V4, P260

[5]

Khasminskii R. Z., 1963, Theory Probab. Appl., V8, P1

[6] A LIMIT THEOREM FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH RANDOM RIGHT-HAND SIDES [J].

KHASMINSKII, RZ .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1966, 11 (03) :390-+

[7]

KOLOMIETS VG, 1991, UKR MATH J, V43, P242

[8]

N'Goran L., 2001, RANDOM OPERATORS STO, V9, P399

[9] 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

[10]

Revuz D., 1999, CONTINUOUS MARTINGAL

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