Two-sided reflection problem for the Markov modulated Brownian motion

Bernardo D'Auria, Offer Kella, Jevgenijs Ivanovs and Michel Mandjes

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: In this paper we consider the two-sided reflection of a Markov modulated Brownian motion by analyzing the spectral properties of the matrix polynomial associated with the generator of the free process. We show how to compute for the general case the Laplace transform of the stationary distribution and the average loss rates at both barriers for the reflected process. This work extends previous partial results by broadening and completing the analysis for the special cases when the spectrum of the generator is nonsemi- simple, and for the delicate case where the asymptotic drift of the process is zero.

Keywords: Two-sided; Skorokhod; reflection; Markov; Modulated; Brownian; Motion (search for similar items in EconPapers)
Date: 2010-10
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:ws104024

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