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...

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...

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...