Criteria for ergodicity of Lévy type operators in dimension one (Q952833)

While the explicit criteria for various types of ergodicity for one-dimensional diffusions have been completely settled [see \textit{Mu-Fa, Chen}, in: Stochastic analysis on large scale interacting systems. Papers from the 11th international conference, Hayama, Japan, July 17--26, 2002 and the international conference on stochastic analysis and statistical mechanics, Kyoto, Japan, July 29--30, 2002. Tokyo: Mathematical Society of Japan. Advanced Studies in Pure Mathematics 39, 89--114 (2004; Zbl 1062.60074)], the author presents some sufficient conditions for the recurrence, the positive recurrence and the exponential ergodicity of one-dimensional Lévy type operators. A number of examples are included, such as the fractional Laplacian operator and the Ornstein-Uhlenbeck type operators.