First passage process of a Markov additive process, with applications to reflection problems
Abstract
In this paper we consider the first passage process of a spectrally negative Markov additive process (MAP). The law of this process is uniquely characterized by a certain matrix function, which plays a crucial role in fluctuation theory. We show how to identify this matrix using the theory of Jordan chains associated with analytic matrix functions. Importantly, our result also provides us with a technique, which can be used to derive various further identities. We then proceed to show how to compute the stationary distribution associated with a one-sided reflected (at zero) MAP for both the spectrally positive and spectrally negative cases as well as for the two sided reflected Markov-modulated Brownian motion; these results can be interpreted in terms of queues with MAP input.
Keywords
Cite
@article{arxiv.1006.2965,
title = {First passage process of a Markov additive process, with applications to reflection problems},
author = {Bernardo D'Auria and Jevgenijs Ivanovs and Offer Kella and Michel Mandjes},
journal= {arXiv preprint arXiv:1006.2965},
year = {2010}
}
Comments
16 pages