Nikola Sandrić
Published 2015-09-03Version 1
In this paper, we study recurrence and transience of L\'evy-type processes, that is, Feller processes associated with pseudo-differential operators. Since the recurrence property of L\'evy-type processes in dimensions greater than two is vacuous and the recurrence and transience of one-dimensional L\'evy-type processes have been very well investigated, in this paper we are focused on the two-dimensional case only. In particular, we study perturbations of two-dimensional L\'evy-type processes which do not affect their recurrence and transience properties, we derive sufficient conditions for their recurrence and transience in terms of the corresponding L\'evy measure and we provide some comparison conditions for the recurrence and transience also in terms of the L\'evy measures.
Comments: arXiv admin note: text overlap with arXiv:1401.2646
Ergodicity of Lévy-Type Processes
On Transience of Lévy-Type Processes
Criteria for the Finiteness of the Strong $p$-Variation for Lévy-type Processes
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