Coupling property and gradient estimates of Lévy processes via the symbol

Abstract

We derive explicitly the coupling property for the transition semigroup of a Lévy process and gradient estimates for the associated semigroup of transition operators. This is based on the asymptotic behaviour of the symbol or the characteristic exponent near zero and infinity, respectively. Our results can be applied to a large class of Lévy processes, including stable Lévy processes, layered stable processes, tempered stable processes and relativistic stable processes.

Published in at http://dx.doi.org/10.3150/11-BEJ375 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

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• On Layered Stable Processes
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Cited by in corpus (11)

• Estimates of transition densities and their derivatives for jump Lévy processes
• Strong convergence of the Euler--Maruyama approximation for a class of Lévy-driven SDEs
• Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes
• Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition
• $L^p$-Wasserstein distance for stochastic differential equations driven by Lévy processes
• Subgeometric rates of convergence for Markov processes under subordination
• Derivative Formula and Harnack Inequality for Linear SDEs Driven by Lévy Processes
• Schauder estimates for equations associated with Lévy generators
• Coupling and Strong Feller for Jump Processes on Banach Spaces
• Existence of densities for stochastic differential equations driven by Lévy processes with anisotropic jumps
• A probabilistic proof of Schoenberg's theorem