Work

Explicit distributions and time-changed dynamics of the two-state Markov modulated Poisson process

Year: 2026

Type: article

Abstract: This paper investigates the two-state Markov modulated Poisson process $$N_t$$ N t , also known as the switched Poisson process. Despite its wide range of applications, a comprehensive characterization of the probability law of $$N_t$$ N t has not been fully addressed in the literature. We contribute to filling this gap by deriving explicit closed-form expressions for the probability distribution and by analyzing its asymptotic behavior. These results also establish a rigorous framework for extensions to more complex dynamics. Specifically, we investigate the time-changed switched Poisson process driven by a subordinator, focusing particularly on the Poisson process and on the inverse stable subordinator. For the latter case, we establish a connection with the fractional Poisson process. Our findings bridge Markov modulated Poisson process theory with fractional dynamics.

Source: Methodology And Computing In Applied Probability

DOI: 10.1007/s11009-026-10327-1

Authors: Nicola Giordano, Barbara Martinucci, Paola Paraggio

Institution: University of Salerno

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per il Calcolo Scientifico