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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Asymptotic behavior of densities of unimodal convolution semigroups


Authors: Wojciech Cygan, Tomasz Grzywny and Bartosz Trojan
Journal: Trans. Amer. Math. Soc. 369 (2017), 5623-5644
MSC (2010): Primary 60J75, 47D06, 60G51; Secondary 44A10, 46F12
DOI: https://doi.org/10.1090/tran/6830
Published electronically: March 31, 2017
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Abstract: We prove the asymptotic formulas for the densities of isotropic unimodal convolution semigroups of probability measures on $ \mathbb{R}^d$ under the assumption that its Lévy-Khintchine exponent is regularly varying of index between 0 and $ 2$.


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Wojciech Cygan
Affiliation: Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Email: wojciech.cygan@uwr.edu.pl

Tomasz Grzywny
Affiliation: Wydział Matematyki, Politechnika Wrocławska, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
Email: tomasz.grzywny@pwr.edu.pl

Bartosz Trojan
Affiliation: Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Email: bartosz.trojan@pwr.edu.pl

DOI: https://doi.org/10.1090/tran/6830
Keywords: Asymptotic formula, L\'evy--Khintchine exponent, heat kernel, Green function, isotropic unimodal L\'evy process, subordinate Brownian motion
Received by editor(s): April 30, 2015
Received by editor(s) in revised form: September 9, 2015
Published electronically: March 31, 2017
Additional Notes: The research of the first author was supported by National Science Centre (Poland), Grant DEC-2013/11/N/ST1/03605
Article copyright: © Copyright 2017 American Mathematical Society

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