04-354 Sergei Kuksin, Armen Shirikyan

On a Ruelle-Perron-Frobenius type theorem (84K, Postscript) Nov 3, 04

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Abstract. We consider the problem of uniqueness of a stationary measure for Markov semigroups on a Polish space. Assuming that the transition function is ``uniformly Feller'' for a family of functions $R$ and uniformly irreducible, we show that any two measures coincide on $R$. In particular, if $R$ is a determining family, then the above conditions ensure the uniqueness of stationary measure. The result obtained has applications in the ergodic theory of randomly forced PDE's.

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