We consider Feller processes on a complete separable metric space X satisfying the ergodic condition of the form$\underset n\rightarrow \infty \to{{\rm lim\,sup}}\left({\textstyle\frac{1}{n}}\sum_{i=1}^{n}P^{i}(x,O)\right)>0\ \text{for some}\ x\in X$, where O is an arbitrary open neighborhood of some point z ∈ X and P is a transition function. It i...

Feller Processes on Nonlocally Compact Spaces

10.1214/009117906000000313