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November 2012 Coupling property and gradient estimates of Lévy processes via the symbol
René L. Schilling, Paweł Sztonyk, Jian Wang
Bernoulli 18(4): 1128-1149 (November 2012). DOI: 10.3150/11-BEJ375


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.


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René L. Schilling. Paweł Sztonyk. Jian Wang. "Coupling property and gradient estimates of Lévy processes via the symbol." Bernoulli 18 (4) 1128 - 1149, November 2012.


Published: November 2012
First available in Project Euclid: 12 November 2012

zbMATH: 1263.60045
MathSciNet: MR2995789
Digital Object Identifier: 10.3150/11-BEJ375

Keywords: coupling , Gradient estimates , Lévy process , symbol

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability


Vol.18 • No. 4 • November 2012
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