Sergei Kuksin, Armen Shirikyan
On a Ruelle-Perron-Frobenius type theorem
(84K, Postscript)
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.