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 ...

Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time. Queuing theory, terminology, and single queue systems are studied with ...

This paper gives easy proofs of conditional limit laws for the population size Z t of a critical Markov branching process whose offspring law is attracted to a stable law with index 1 + α, where 0 ≤ α ...

Probabilistic model checking and Markov decision processes (MDPs) form two interlinked branches of formal analysis for systems operating under uncertainty. These techniques offer a mathematical ...