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Long-time behavior for a class of Feller processes


Author: Nikola Sandrić
Journal: Trans. Amer. Math. Soc. 368 (2016), 1871-1910
MSC (2010): Primary 60J75, 60J25, 60G17
Published electronically: June 24, 2015
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Abstract: In this paper, as a main result, we derive a Chung-Fuchs type condition for the recurrence of Feller processes associated with pseudo-differential operators. In the Lévy process case, this condition reduces to the classical and well-known Chung-Fuchs condition. Further, we also discuss the recurrence and transience of Feller processes with respect to the dimension of the state space and Pruitt indices and the recurrence and transience of Feller-Dynkin diffusions and stable-like processes. Finally, in the one-dimensional symmetric case, we study perturbations of Feller processes which do not affect their recurrence and transience properties, and we derive sufficient conditions for their recurrence and transience in terms of the corresponding Lévy measure. In addition, some comparison conditions for recurrence and transience also in terms of the Lévy measures are obtained.


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Additional Information

Nikola Sandrić
Affiliation: Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, 10000 Zagreb, Croatia
Email: nsandric@grad.hr

DOI: https://doi.org/10.1090/tran/6371
Keywords: Feller process, Feller-Dynkin diffusion, L\'evy measure, Pruitt indices, recurrence, stable-like process, symbol, transience
Received by editor(s): August 18, 2013
Received by editor(s) in revised form: November 11, 2013, December 9, 2013, and January 8, 2014
Published electronically: June 24, 2015
Article copyright: © Copyright 2015 American Mathematical Society