scholarly journals A transience condition for a class of one-dimensional symmetric Lévy processes

2013 ◽  
Vol 18 (0) ◽  
Author(s):  
Nikola Sandrić
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
One Dimensional ◽  
Transience Condition

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.

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 ∞.

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

2000 ◽  
Vol 32 (2) ◽  
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.

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