Journals / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 3
The cyclic behavior of the constrictive Markov operators
- Pages
- 540–550
- DOI
- —
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.
Özet
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.