The Annals of Probability

Feller processes on nonlocally compact spaces

Tomasz Szarek

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Abstract

We consider Feller processes on a complete separable metric space X satisfying the ergodic condition of the form

\[\mathop{\lim\sup}_{n\rightarrow\infty}\Biggl(\frac{1}{n}\sum_{i=1}^{n}P^{i}(x,O)\Biggr)>0\qquad\mbox{for some }x\in X,\]

where O is an arbitrary open neighborhood of some point zX and P is a transition function. It is shown that e-chains which satisfy the above condition admit an invariant probability measure. Some results on the stability of such processes are also presented.

Article information

Source
Ann. Probab., Volume 34, Number 5 (2006), 1849-1863.

Dates
First available in Project Euclid: 14 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.aop/1163517227

Digital Object Identifier
doi:10.1214/009117906000000313

Mathematical Reviews number (MathSciNet)
MR2271485

Zentralblatt MATH identifier
1108.60064

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 37A30: Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35}

Keywords
e-chain invariant measure stability

Citation

Szarek, Tomasz. Feller processes on nonlocally compact spaces. Ann. Probab. 34 (2006), no. 5, 1849--1863. doi:10.1214/009117906000000313. https://projecteuclid.org/euclid.aop/1163517227


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