On transience of Lévy-type processes. Issue 7 (2nd October 2016)

• Record Type: Journal Article
• Authors: Sandrić, Nikola
• Is Part Of: Stochastics. Volume 88:Issue 7(2016)
• Page Start: 1012
• Page End: 1040
• Publication Date: 2016-10-02
• Subjects: Lévy-type process -- strong transience -- symbol -- transience -- weak transience; 60J25 -- 60J75 -- 60G17; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2016.1178749
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : In this paper, we study weak and strong transience of a class of Feller processes associated with pseudo-differential operators, the so-called Lévy-type processes. As a main result, we derive Chung-Fuchs type conditions (in terms of the symbol of the corresponding pseudo-differential operator) for these properties, which are sharp for Lévy processes. Also, as a consequence, we discuss the weak and strong transience with respect to the dimension of the state space and Pruitt indices, thus generalizing some well-known results related to elliptic diffusion and stable Lévy processes. Finally, in the case when the symbol is radial (in the co-variable) we provide conditions for the weak and strong transience in terms of the Lévy measures.