On Limiting Behavior of Stationary Measures for Stochastic Evolution Systems with Small Noise Intensity\@textsuperscript\safe@setrefT1thanksT1\@nil,\safe@setrefT1thanks\@nil\@@T1,\safe@setrefT1thanks
The limiting behavior of stochastic evolution processes with small noise intensity is investigated in distribution-based approach. Let be stationary measure for stochastic process with small and be a semiflow on a Polish space. Assume that is tight. Then all their limits in weak sense are invariant and their supports are contained in Birkhoff center of . Applications are made to various stochastic evolution systems, including stochastic ordinary differential equations, stochastic partial differential equations, stochastic functional differential equations driven by Brownian motion or Lévy process.