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On the existence and explicit estimates for the coupling property of Lévy processes with drift. (English) Zbl 1301.60069

Summary: 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 H.-N. Lin and J. Wang [Sci. China, Math. 55, No. 8, 1735–1748 (2012; Zbl 1274.60241)]. 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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G51 Processes with independent increments; Lévy processes
60J25 Continuous-time Markov processes on general state spaces
60J75 Jump processes (MSC2010)

Citations:

Zbl 1274.60241
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References:

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