Interaction of particles governed by generalized integrated telegraph processes

Abstract

Abstract In this paper we introduce the analysis of the interaction of two or more particles, where each of them is governed by a generalized integrated telegraph process. We present systematically the distribution of the meeting instant of two telegraph particles on the line (or collision phenomenon) that started their motion at the same time but from different locations. We also investigate the distribution of a switching time such that there exists the first moment of the first instant of two particles collision. Asymptotic results of particle collisions for a system of interacting particles with Markov switching, as time goes to infinity, are considered.