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Stability with a general rate function for a class of stochastic evolution equations in infinite dimensional spaces

Part of: Stochastic systems and control Stochastic analysis

Published online by Cambridge University Press:  09 April 2009

Kai Liu
Kai Liu
Affiliation:
Department of Statistics and Modelling Science University of StrathclydeGlasgow G1 1XH, ScotlandU. K. e-mail address: kai@stams.strath.ac.uk
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Abstract

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The aim of this paper is to investigate the almost sure stability with a certain rate function λ(t) for a class of stochastic evolution equations in infinite dimensional spaces under various sufficient conditions. The results obtained here include exponential and polynomial stability as special cases. Much more refined sufficient conditions than the usual ones, for example, those described in [14], are obtained under our framework by the method of Liapunov functions. Two examples are given to illustrate our theory.

MSC classification

Secondary: 93E03: Stochastic systems, general 60H10: Stochastic ordinary differential equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 1 , August 1997 , pp. 128 - 144
Copyright
Copyright © Australian Mathematical Society 1997

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