ALMOST SURE ASYMPTOTIC STABILITY OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH JUMPS

被引：16

作者：

Bao, Jianhai ^{[1
,2
]}

Truman, Aubrey ^{[2
]}

Yuan, Chenggui ^{[1
,2
]}

机构：

[1] Cent S Univ, Sch Math, Changsha 410075, Hunan, Peoples R China

[2] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2011年 / 49卷 / 02期

关键词：

stochastic partial differential equations; jump processes; Khasminskii-type theorem; almost sure asymptotic stability; EVOLUTION-EQUATIONS; STATIONARY SOLUTIONS; BURGERS-EQUATION; DELAY EQUATIONS; UNIQUENESS; EXISTENCE; DRIVEN;

D O I：

10.1137/100786812

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper we investigate stochastic partial differential equations with jumps in infinite dimensions. The key motivation of this paper is, under a local Lipschitz condition but without a linear growth condition, to give an existence-and-uniqueness theorem (Khasminskii-type theorem), where the classical existence-and-uniqueness result can be regarded as a special case, and then to discuss the almost sure asymptotic stability of the solutions. Moreover, as a by-product, we also derive that the solutions are weakly attracted. Finally, several examples are constructed to demonstrate our results.

引用

页码：771 / 787

页数：17

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