Long-time behaviour of nonautonomous SPDE's

Bohdan Maslowski and Isabel Simão

Stochastic Processes and their Applications, 2001, vol. 95, issue 2, 285-309

Abstract: It is proved that under suitable conditions the probability laws of two arbitrary solutions of the infinite dimensional stochastic equationdXt=AXt dt+f(t,Xt) dt+Q1/2 dWtconverge to each other, as time goes to infinity, in the strong (variational) topology. To this end, some lower estimates on the transition density of the solution, with respect to a certain Gaussian measure, are obtained. In addition, an explicit formula for the density is given, in the case where Q-1/2f is bounded.

Keywords: SPDE's; Markov; processes; Transition; densities; Asymptotic; stability (search for similar items in EconPapers)
Date: 2001
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