Physical Sciences and Mathematics Commons^™

The Cyclic Behavior Of The Constrictive Markov Operators, César Emilio Villarreal Rodríguez

Turkish Journal of Mathematics

Let S be a Polish space, and let M_{\varSigma} be the Banach space of finite signed measures on the Borel \Sigma-algebra \varSigma of S. Given a constrictive Markov operator T:M_{\varSigma}\rightarrow M_{\varSigma}, we use the asymptotic periodic decomposition of T to determine the set of T-invariant distributions in M_{\varSigma} and the set of T-ergodic distributions. We also give the relationship between the asymptotic periodic decomposition and the cycles of the process relative to the operator T.