Coupling Property and Gradient Estimates of Lévy Processes via the Symbol

Details Coupling Property and Gradient Estimates of Lévy Processes via the Symbol Coupling Property and Gradient Estimates of Lévy Processes via the Symbol

2010-11-04

arxiv.org/abs/1011.1067v2

Mathematics

Probability

19 Pages

Scientific paper

We derive explicitly the coupling property for the transition semigroup of a L\'evy 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 L\'evy processes, including stable L\'evy processes, layered stable processes, tempered stable processes and relativistic stable processes.

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