Singularities of the matrix exponent of a Markov additive process with one-sided jumps
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| Publication date | 2010 |
| Journal | Stochastic Processes and their Applications |
| Volume | Issue number | 120 | 9 |
| Pages (from-to) | 1776-1794 |
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| Abstract | We analyze the number of zeros of det(F(α)), where F(α) 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(α) 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. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1016/j.spa.2010.05.007 |
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Mandjes_Ivanovs_SPA_2010.pdf
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