Open Access
November 2020 Lévy processes: Concentration function and heat kernel bounds
Tomasz Grzywny, Karol Szczypkowski
Bernoulli 26(4): 3191-3223 (November 2020). DOI: 10.3150/20-BEJ1220


We investigate densities of vaguely continuous convolution semigroups of probability measures on the Euclidean space. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are equivalent to the behaviour of the maximum of the density as a function of time variable. We also prove qualitative lower estimates under mild assumptions on the corresponding jump measure and the characteristic exponent.


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Tomasz Grzywny. Karol Szczypkowski. "Lévy processes: Concentration function and heat kernel bounds." Bernoulli 26 (4) 3191 - 3223, November 2020.


Received: 1 July 2019; Revised: 1 March 2020; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256173
MathSciNet: MR4140542
Digital Object Identifier: 10.3150/20-BEJ1220

Keywords: Heat kernel estimates , Lévy process , Non-local operator , non-symmetric Markov process , non-symmetric operator , semigroups of measures , Transition density

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 4 • November 2020
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