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Lyapunov-type conditions for stationary distributions of diffusion processes on Hilbert spaces. (English) Zbl 0828.60063

Summary: We apply the method of Lyapunov functions to differential operators associated with diffusion processes in Hilbert spaces in order to ensure existence and uniqueness of stationary distributions and their attractivity. We restrict matters to the case of coefficients that are everywhere defined and derive our results from more general ones on completely regular Radon spaces. We also give an example of nonuniqueness and apply these results to systems of scalar, interacting, stochastic differential equations.

MSC:

60J60 Diffusion processes
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