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math.PR2026
Exit problems for additive-increase and multiplicative-decrease Markov-modulated processes
Bernardo D'Auria, Zbigniew Palmowski
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-jum…
math.PR2026
A class of Markov processes with resetting and applications to cybersecurity
Giorgia Callegaro, Umut Çetin, Bernardo D'Auria
We introduce a class of piecewise deterministic Markov processes with resetting, motivated by self-exciting models of cyber attacks. Under assumptions reminiscent of ruin theory, w…