On Limiting Behavior of Stationary Measures for Stochastic Evolution Systems with Small Noise Intensity\@textsuperscript\safe@setrefT1thanksT1\@nil,\safe@setrefT1thanks\@nil\@@T1,\safe@setrefT1thanks

On Limiting Behavior of Stationary Measures for Stochastic Evolution Systems with Small Noise Intensity\@textsuperscript\safe@setrefT1thanksT1\@nil,\safe@setrefT1thanks\@nil\@@T1,\safe@setrefT1thanks

\fnmsLifeng \snmChen    \fnmsZhao \snmDong    \fnmsJifa \snmJiang\@textsuperscript\safe@setreft1thankst1\@nil,\safe@setreft1thanks\@nil\@@t1,\safe@setreft1thanks    \fnmsJianliang \snmZhai

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.

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