Semi-Lévy processes, semi-selfsimilar additive processes, and semi-stationary Ornstein-Uhlenbeck type processes

Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and nondefective processes, and all possible scenarios, we identify the corresponding potential measures, which help to generalize a number of results for one-sided Lévy processes. The resulting rather neat formulae have various applications in risk and queueing theories, and, in particular, they lead to quasistationary distributions of the corresponding processes.

Download Full-text

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

Advances in Applied Probability ◽

10.1017/s0001867800009988 ◽

2000 ◽

Vol 32 (02) ◽

pp. 376-393 ◽

Cited By ~ 12

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.

Download Full-text

Potential Measures of One-Sided Markov Additive Processes with Reflecting and Terminating Barriers

Journal of Applied Probability ◽

10.1017/s0021900200012031 ◽

2014 ◽

Vol 51 (04) ◽

pp. 1154-1170 ◽

Cited By ~ 2

Author(s):

Jevgenijs Ivanovs

Keyword(s):

Lévy Processes ◽

Levy Processes ◽

Additive Process ◽

Markov Additive Process ◽

Additive Processes ◽

Quasistationary Distributions ◽

Markov Additive Processes

Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and nondefective processes, and all possible scenarios, we identify the corresponding potential measures, which help to generalize a number of results for one-sided Lévy processes. The resulting rather neat formulae have various applications in risk and queueing theories, and, in particular, they lead to quasistationary distributions of the corresponding processes.

Download Full-text

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

Advances in Applied Probability ◽

10.1239/aap/1013540169 ◽

2000 ◽

Vol 32 (2) ◽

pp. 376-393 ◽

Cited By ~ 57

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.

Download Full-text

Potential Measures of One-Sided Markov Additive Processes with Reflecting and Terminating Barriers

Journal of Applied Probability ◽

10.1239/jap/1421763333 ◽

2014 ◽

Vol 51 (4) ◽

pp. 1154-1170 ◽

Cited By ~ 5

Author(s):

Jevgenijs Ivanovs

Keyword(s):

Lévy Processes ◽

Levy Processes ◽

Additive Process ◽

Markov Additive Process ◽

Additive Processes ◽

Quasistationary Distributions ◽

Markov Additive Processes

Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and nondefective processes, and all possible scenarios, we identify the corresponding potential measures, which help to generalize a number of results for one-sided Lévy processes. The resulting rather neat formulae have various applications in risk and queueing theories, and, in particular, they lead to quasistationary distributions of the corresponding processes.

Download Full-text