Abstract
In this paper we consider exponentially asymptotic stability in the p-th mean of the equilibrium mild solution to a semilinear stochastic evolution equation in a separable Hilbert space H and discuss under what conditions any mild solution approaches exponentially the equilibrium mild solution, almost surely. We shall generalize Haussmann's results [J. Math. Anal. Appl., 65 (1978), 219-235]. For illustrating the theorems we consider a semilinear stochastic heat equation
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