Speaker: Nicola Giordano (University of Salerno)
Title: On the switched Poisson process and its compound version
Abstract: In this talk, we analyze the switched Poisson process Nt, a Markov modulated Poisson process governed by a two-state Markov chain. Despite its wide range of applications, a comprehensive study of the probability law of Nt has been lacking in the literature. We address this gap by deriving explicit expressions for the probability law of Nt and investigating its behavior for limiting values of the parameters and specific parameter combinations of interest. In particular, we discuss both a stationary and an interval-stationary version of Nt, providing closed-form expressions for its probability distribution and moments. These results further allow us to study a compound switched Poisson process by considering different jump size distributions, including both discrete and absolutely continuous cases.
The talk is based on joint work with Barbara Martinucci and Paola Paraggio.
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