ON EXPONENTIAL STABILITY OF NON-AUTONOMOUS STOCHASTIC SEMILINEAR EVOLUTION EQUATIONS

Abstract

Abstract:

Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analy-sis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with
exponential decay. Lastly, two examples are investigated to illustrate the theory.

Key words: Non-autonomous stochastic evolution equations, mean square exponential stability, almost sure exponential stability

CLC Number:

60H15

XIA Xue-Wen, LIU Kai. ON EXPONENTIAL STABILITY OF NON-AUTONOMOUS STOCHASTIC SEMILINEAR EVOLUTION EQUATIONS[J].Acta mathematica scientia,Series B, 2002, 22(2): 178-188.

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