Coupling property and gradient estimates of L\'{e}vy processes via the symbol
Probability
2012-12-06 v3 Functional Analysis
Statistics Theory
Statistics Theory
Abstract
We derive explicitly the coupling property for the transition semigroup of a L\'{e}vy 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\'{e}vy processes, including stable L\'{e}vy processes, layered stable processes, tempered stable processes and relativistic stable processes.
Keywords
Cite
@article{arxiv.1011.1067,
title = {Coupling property and gradient estimates of L\'{e}vy processes via the symbol},
author = {René L. Schilling and Paweł Sztonyk and Jian Wang},
journal= {arXiv preprint arXiv:1011.1067},
year = {2012}
}
Comments
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)