Turkish Journal of Mathematics
Abstract
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.
DOI
10.3906/mat-1102-5
Keywords
Asymptotically periodic, constrictive operator, cyclic decomposition, ergodic decomposition, ergodic measure, Harris decomposition, invariant measure
First Page
540
Last Page
550
Recommended Citation
RODRÍGUEZ, C. E (2013). The cyclic behavior of the constrictive Markov operators. Turkish Journal of Mathematics 37 (3): 540-550. https://doi.org/10.3906/mat-1102-5
