Feller processes on nonlocally compact spaces

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 z∈X 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.