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, CÉSAR EMILIO VILLARREAL
(2013)
"The cyclic behavior of the constrictive Markov operators,"
Turkish Journal of Mathematics: Vol. 37:
No.
3, Article 15.
https://doi.org/10.3906/mat-1102-5
Available at:
https://journals.tubitak.gov.tr/math/vol37/iss3/15
