Khasminskii-Type Theorem and LaSalle-Type Theorem for Stochastic Evolution Delay Equations

Jianhai Bao; Xuerong Mao; Chenggui Yuan

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arXiv · 1002.3116

Khasminskii-Type Theorem and LaSalle-Type Theorem for Stochastic Evolution Delay Equations

Jianhai Bao·Xuerong Mao·Chenggui Yuan

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Abstract

In this paper we study the well-known Khasminskii-Type Theorem, i.e. the existence and uniqueness of solutions of stochastic evolution delay equations, under local Lipschitz condition, but without linear growth condition. We then establish one stochastic LaSalle-type theorem for asymptotic stability analysis of strong solutions. Moreover, several examples are established to illustrate the power of our theories.

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BibTeX RIS

Jianhai Bao, Xuerong Mao, Chenggui Yuan. 2010-02-16. Khasminskii-Type Theorem and LaSalle-Type Theorem for Stochastic Evolution Delay Equations. https://arxiv.org/abs/1002.3116

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