After having worked in the domain of Gaussian queues for about a decade, we got the idea
to look at similar problems, but now in the context of Lévy-driven queues. That step felt as …

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 …

Markov-modulated fluids have a long history. They form a simple class of Markov additive
processes, and were initially developed in the 1950s as models for dams and reservoirs …

This survey addresses the class of queues with Lévy input, which covers the classical M/G/1
queue and the reflected Brownian motion as special cases. First the stationary behavior is …

We consider a Markov-modulated Brownian motion reflected to stay in a strip [0, B]. The
stationary distribution of this process is known to have a simple form under some …

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 …

This paper considers a Cramér–Lundberg risk setting, where the components of the
underlying model change over time. We allow the more general setting of the cumulative …

Abstract We prove the Wiener–Hopf factorization for Markov additive processes. We derive
also Spitzer–Rogozin theorem for this class of processes which serves for obtaining …

We study the first passage process of a spectrally negative Markov additive process (MAP).
The focus is on the background Markov chain at the times of the first passage. This process …

This survey addresses the class of queues with Lévy input, which covers the classical M/G/1
queue and reflected Brownian motion as special cases. First the stationary behavior is …