Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156890 | Stochastic Processes and their Applications | 2010 | 19 Pages |
Abstract
We analyze the number of zeros of det(F(α))det(F(α)), where F(α)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)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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jevgenijs Ivanovs, Onno Boxma, Michel Mandjes,