On the record process of time-reversible spectrally-negative Markov additive processes

We study the record process of a spectrally-negative Markov additive process (MAP). Assuming time-reversibility, a number of key quantities can be given explicitly. It is shown how these key quantities can be used when analyzing the distribution of the all-time maximum attained by MAPs with negative drift, or, equivalently, the stationary workload distribution of the associated storage system; the focus is on Markov-modulated Brownian mo- tion, spectrally-negative and spectrally-positive MAPs. It is also argued how our results are of great help in the numerical analysis of systems in which the driving MAP is a superposition of multiple time-reversible MAPs.