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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Long-time behavior for a class of Feller processes
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by Nikola Sandrić PDF
Trans. Amer. Math. Soc. 368 (2016), 1871-1910 Request permission

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
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 1871-1910
  • MSC (2010): Primary 60J75, 60J25, 60G17
  • DOI: https://doi.org/10.1090/tran/6371
  • MathSciNet review: 3449227