Absolute continuity of distributions of one-dimensional Lévy processes

2017 ◽  
Vol 54 (3) ◽  
pp. 852-872
Author(s):  
Tongkeun Chang
Keyword(s):  
Absolute Continuity ◽  
Lévy Processes ◽  
Levy Processes ◽  
Previous Literature ◽  
One Dimensional ◽  
The Absolute

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 ∞.

scholarly journals On the absolute continuity of Lévy processes with drift

2006 ◽  
Vol 34 (3) ◽  
pp. 1035-1051 ◽  
Author(s):  
Ivan Nourdin ◽  
Thomas Simon
Keyword(s):  
Absolute Continuity ◽  
Lévy Processes ◽  
Levy Processes ◽  
The Absolute

scholarly journals A Variant of the Necessary Condition for the Absolute Continuity of Symmetric Multivariate Mixture

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1505
Author(s):  
Evgeniy Anatolievich Savinov
Keyword(s):  
Absolute Continuity ◽  
Joint Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Necessary Condition ◽  
Conditional Distributions ◽  
One Dimensional ◽  
The Absolute

Sufficient conditions are given under which the absolute continuity of the joint distribution of conditionally independent random variables can be violated. It is shown that in the case of a dimension n>1 this occurs for a sufficiently large number of discontinuity points of one-dimensional conditional distributions.

A multi-dimensional martingale for Markov additive processes and its applications

2000 ◽  
Vol 32 (02) ◽  
pp. 376-393 ◽  
Author(s):  
Søren Asmussen ◽  
Offer Kella
Keyword(s):  
Brownian Motion ◽  
Lévy Processes ◽  
Levy Processes ◽  
One Dimensional ◽  
Additive Processes ◽  
Motion Models ◽  
And Brownian Motion ◽  
Storage Processes ◽  
Reflecting Barriers ◽  
Markov Additive Processes

We establish new multidimensional martingales for Markov additive processes and certain modifications of such processes (e.g., such processes with reflecting barriers). These results generalize corresponding one-dimensional martingale results for Lévy processes. This martingale is then applied to various storage processes, queues and Brownian motion models.

Sign in / Sign up

Export Citation Format

Share Document