Stability in terms of two measures of solutions to stochastic partial differential delay equations with switching

2016/09/06 by Shufen Zhao, Zhao, Shufen, Minghui Song +1
Mathematics · #93E03 #93E15 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:93E03 #msc:93E15

paper · pdf · doi:10.48550/arxiv.1609.01486

arxiv created 2016/09/06 · arxiv updated 2016/09/07

Abstract

In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on the technique of constructing a proper approximating strong solution system and carrying out a limiting type of argument to pass on stability of strong solutions to mild ones obtained by Bao, Truman and Yuan [ J. Bao, A. Truman,C. Yuan, Stability in distribution of mild solutions to stochastic partial differential delay equations with jumps, Proc. R. Soc. A, 465, 2111-2134 (2009)]. In particular, the stochastic stability under the fixed-index sequence monotonicity condition and under the average dwell-time switching are considered.

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