Abstract
We investigate stationary distributions of diffusion processes on Hilbert spaces by means of Lyapunov functions: existence, uniqueness, and attractivity. The emphasis is on solutions to stochastic differential equations with nonlinear diffusion coefficients and unbounded and nonlinear drift. The methods are applicable to stochastic partial differential equations such as multidimensional stochastic reaction–diffusion equations. The method provides also information on the supports of the stationary distributions.
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