On the Coupling Property of Lévy Processes

Abstract

We give necessary and sufficient conditions guaranteeing that the coupling for Lévy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall-Rogers on couplings of random walks. In particular, we obtain that a Lévy process admits a successful coupling, if it is a strong Feller process or if the Lévy (jump) measure has an absolutely continuous component.

14 pages

Cited by in corpus (6)

• Coupling property and gradient estimates of Lévy processes via the symbol
• Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes
• $L^p$-Wasserstein distance for stochastic differential equations driven by Lévy processes
• Derivative Formula and Harnack Inequality for Linear SDEs Driven by Lévy Processes
• Coupling and Strong Feller for Jump Processes on Banach Spaces
• Constructing Maximal Germ Couplings of Brownian Motions with Drift