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Absolute continuity of distributions of one-dimensional Lévy processes

Part of: Integral operators Miscellaneous topics of analysis in the complex domain

Published online by Cambridge University Press:  15 September 2017

Tongkeun Chang
Tongkeun Chang*
Affiliation:
Yonsei University
*
* Postal address: Department of Mathematics, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul, 03722, Korea. Email address: chang7357@yonsei.ac.kr
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Abstract

In this paper we study the existence of Lebesgue densities of one-dimensional Lévy processes. Equivalently, we show the absolute continuity of the distributions of one-dimensional Lévy processes. Compared with the previous literature, we consider Lévy processes with Lévy symbols of a logarithmic behavior at ∞.

Keywords

Lévy processLebesgue densitysubordinator

MSC classification

Primary: 45P05: Integral operators
Secondary: 30E25: Boundary value problems
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 852 - 872
Copyright
Copyright © Applied Probability Trust 2017 

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