scholarly journals Front propagation and quasi-stationary distributions for one-dimensional Lévy processes

2018 ◽  
Vol 23 ◽  
Author(s):  
Pablo Groisman ◽  
Matthieu Jonckheere
Keyword(s):  
Lévy Processes ◽  
Front Propagation ◽  
Levy Processes ◽  
Stationary Distributions ◽  
One Dimensional

Periodic Ornstein-Uhlenbeck processes driven by Lévy processes

2002 ◽  
Vol 39 (04) ◽  
pp. 748-763 ◽  
Author(s):  
Jan Pedersen
Keyword(s):  
Stationary Distribution ◽  
Random Fields ◽  
Markov Random Fields ◽  
Lévy Processes ◽  
Levy Processes ◽  
Uhlenbeck Process ◽  
Stationary Distributions ◽  
Markov Random ◽  
Ornstein Uhlenbeck Process

In this paper, the class of periodic Ornstein-Uhlenbeck processes is defined. It is shown that periodic Ornstein-Uhlenbeck processes are stationary Markov random fields and the class of stationary distributions is characterized. In particular, any self-decomposable distribution is the stationary distribution of some periodic Ornstein-Uhlenbeck process. As examples, gamma periodic Ornstein-Uhlenbeck processes and Gaussian periodic Ornstein-Uhlenbeck processes are considered.

scholarly journals Quasi-stationary distributions for Lévy processes

Bernoulli ◽  
2006 ◽  
Vol 12 (4) ◽  
pp. 571-581 ◽  
Author(s):  
Andreas E. Kyprianou ◽  
Zbigniew Palmowski
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Stationary Distributions

Periodic Ornstein-Uhlenbeck processes driven by Lévy processes

2002 ◽  
Vol 39 (4) ◽  
pp. 748-763 ◽  
Author(s):  
Jan Pedersen
Keyword(s):  
Stationary Distribution ◽  
Random Fields ◽  
Markov Random Fields ◽  
Lévy Processes ◽  
Levy Processes ◽  
Uhlenbeck Process ◽  
Stationary Distributions ◽  
Markov Random ◽  
Ornstein Uhlenbeck Process

In this paper, the class of periodic Ornstein-Uhlenbeck processes is defined. It is shown that periodic Ornstein-Uhlenbeck processes are stationary Markov random fields and the class of stationary distributions is characterized. In particular, any self-decomposable distribution is the stationary distribution of some periodic Ornstein-Uhlenbeck process. As examples, gamma periodic Ornstein-Uhlenbeck processes and Gaussian periodic Ornstein-Uhlenbeck processes are considered.

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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