The cyclic behavior of the constrictive Markov operators

Authors : Ceésar Emilio VILLARREAL-RODRÍGUEZ

Pages : 540-550

Doi:10.3906/mat-1102-5

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let S be a Polish space, and let M\varSigma be the Banach space of finite signed measures on the Borel S-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.
Keywords : Asymptotically periodic, constrictive operator, cyclic decomposition, ergodic decomposition, ergodic measure, Harris decomposition, invariant measure