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Extensions of Regularity for a Levy Process

Date

Authors

Maller, Ross

Publisher

Society for Industrial and Applied Mathematics

Abstract

We obtain necessary and sufficient conditions for the finiteness of certain moment functions of the random variable T0(-), which is the first passage time of a Levy process (X-t)(t >= 0) below zero, and the position XT0- of the process at this time. Our results generalize classical results of Rogozin and Bertoin on the regularity of X, and extend earlier results of Blumenthal and Getoor on the regularity index.

Keywords

regularity of a real-valued L´evy process, dominance of the positive part of a L´evy process over the negative part, first passage of a L´evy process below zero, first passage time, dominated variation conditions, Rogozin regularity condition

URI

http://hdl.handle.net/1885/229850

Collections

ANU Research Publications

Source

Theory of Probability and its Applications

Type

Journal article

Access Statement

Open Access

DOI

10.1137/S0040585X97T988824

Downloads

File

Description

01_Maller_Extensions_of_Regularity_for_a_2018.pdf (295.86 KB)