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

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.