Singularities of the matrix exponent of a Markov additive process with one-sided jumps

Jevgenijs Ivanovs, Onno Boxma and Michel Mandjes

Stochastic Processes and their Applications, 2010, vol. 120, issue 9, 1776-1794

Abstract: We analyze the number of zeros of det(F([alpha])), where F([alpha]) is the matrix exponent of a Markov Additive Process (MAP) with one-sided jumps. The focus is on the number of zeros in the right half of the complex plane, where F([alpha]) is analytic. In addition, we also consider the case of a MAP killed at an independent exponential time. The corresponding zeros can be seen as the roots of a generalized Cramér-Lundberg equation. We argue that our results are particularly useful in fluctuation theory for MAPs, which leads to numerous applications in queueing theory and finance.

Keywords: Markov; additive; processes; Lévy; processes; Queueing; theory; Markov; modulation; First; passage; Roots; of; Cramer-Lundberg; equation; Argument; principle (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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