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

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

2010-02-16

arxiv.org/abs/1002.3116v1

Mathematics

Probability

Scientific paper

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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