Bernardo D'Auria

Exit problems for additive-increase and multiplicative-decrease Markov-modulated processes

We study one-sided, two-sided and reflected exit problems for a finite-state Markov-modulated additive-increase and multiplicative-decrease process. For upward passage, a first-jump decomposition and a spatial Laplace transform lead to a recursion indexed by finite words of phases and to a convergent Green series. For...