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September 2006 Feller processes on nonlocally compact spaces
Tomasz Szarek
Ann. Probab. 34(5): 1849-1863 (September 2006). DOI: 10.1214/009117906000000313


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.


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Tomasz Szarek. "Feller processes on nonlocally compact spaces." Ann. Probab. 34 (5) 1849 - 1863, September 2006.


Published: September 2006
First available in Project Euclid: 14 November 2006

zbMATH: 1108.60064
MathSciNet: MR2271485
Digital Object Identifier: 10.1214/009117906000000313

Primary: 60J05
Secondary: 37A30

Keywords: e-chain , invariant measure , stability

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 5 • September 2006
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