Two-sided reflection of Markov-modulated brownian motion

B. D'Auria; J. Ivanovs; O. Kella; M. Mandjes

doi:10.1080/15326349.2012.672285

Two-sided reflection of Markov-modulated brownian motion

B. D'Auria^*, J. Ivanovs, O. Kella, M. Mandjes

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

This article considers a Markov-modulated Brownian motion with a two-sided reflection. For this doubly-reflected process we compute the Laplace transform of the stationary distribution, as well as the average loss rates at both barriers. Our approach relies on spectral properties of the matrix polynomial associated with the generator of the free (that is, non-reflected) process. This work generalizes previous partial results allowing the spectrum of the generator to be non-semi-simple and also covers the delicate case where the asymptotic drift of the free process is zero.

Original language	English
Pages (from-to)	316-332
Number of pages	17
Journal	Stochastic Models
Volume	28
Issue number	2
DOIs	https://doi.org/10.1080/15326349.2012.672285
State	Published - 1 Apr 2012

Bibliographical note

Funding Information:
The first author is partially supported by the Spanish Ministry of Education and Science Grants MTM2007-63140, SEJ2007-64500 and MTM2010-16519. Part of his research was done when he was visiting the Hebrew University of Jerusalem by partial support of Madrid University Carlos III Grant for Young Researchers’ Mobility. The third author is partially supported by grant 964/06 from the Israel Science Foundation and the Vigevani Chair in Statistics.

Keywords

Markov additive process
Markov-modulated Brownian motion
Skorohod reflection
Two-sided reflection

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10.1080/15326349.2012.672285

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title = "Two-sided reflection of Markov-modulated brownian motion",

abstract = "This article considers a Markov-modulated Brownian motion with a two-sided reflection. For this doubly-reflected process we compute the Laplace transform of the stationary distribution, as well as the average loss rates at both barriers. Our approach relies on spectral properties of the matrix polynomial associated with the generator of the free (that is, non-reflected) process. This work generalizes previous partial results allowing the spectrum of the generator to be non-semi-simple and also covers the delicate case where the asymptotic drift of the free process is zero.",

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AU - Kella, O.

AU - Mandjes, M.

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N2 - This article considers a Markov-modulated Brownian motion with a two-sided reflection. For this doubly-reflected process we compute the Laplace transform of the stationary distribution, as well as the average loss rates at both barriers. Our approach relies on spectral properties of the matrix polynomial associated with the generator of the free (that is, non-reflected) process. This work generalizes previous partial results allowing the spectrum of the generator to be non-semi-simple and also covers the delicate case where the asymptotic drift of the free process is zero.

AB - This article considers a Markov-modulated Brownian motion with a two-sided reflection. For this doubly-reflected process we compute the Laplace transform of the stationary distribution, as well as the average loss rates at both barriers. Our approach relies on spectral properties of the matrix polynomial associated with the generator of the free (that is, non-reflected) process. This work generalizes previous partial results allowing the spectrum of the generator to be non-semi-simple and also covers the delicate case where the asymptotic drift of the free process is zero.

KW - Markov additive process

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Two-sided reflection of Markov-modulated brownian motion

Abstract

Bibliographical note

Keywords

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