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On the Existence and Explicit Estimates for the Coupling Property of Lévy Processes with Drift

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  • Jian Wang

    (Fujian Normal University)

Abstract

In this article, we first establish new criteria for the coupling property of Lévy processes with drift. The criteria are sharp for Lévy processes and Ornstein-Uhlenbeck processes with jumps, and also strengthen the recent result of Lin and Wang (Sci China Math 55:1735–1748, Theorem 1.1, 2012). Then, using the time-change technique, we derive explicit estimates for the coupling property of subordinated Brownian motions with drift. These estimates are optimal for a large class of subordinated Brownian motions.

Suggested Citation

  • Jian Wang, 2014. "On the Existence and Explicit Estimates for the Coupling Property of Lévy Processes with Drift," Journal of Theoretical Probability, Springer, vol. 27(3), pages 1021-1044, September.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:3:d:10.1007_s10959-012-0463-y
    DOI: 10.1007/s10959-012-0463-y
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    References listed on IDEAS

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    1. Wang, Jian, 2010. "Regularity of semigroups generated by Lévy type operators via coupling," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1680-1700, August.
    2. Böttcher, Björn & Schilling, René L. & Wang, Jian, 2011. "Constructions of coupling processes for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1201-1216, June.
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