Telegraph random evolutions on a circle

Alessandro De Gregorio and Francesco Iafrate

Stochastic Processes and their Applications, 2021, vol. 141, issue C, 79-108

Abstract: We consider the random evolution described by the motion of a particle moving on a circle alternating the angular velocities ±c and changing rotation at Poisson random times, resulting in a telegraph process over the circle. We study the analytic properties of the semigroup it generates as well as its probability distribution. The asymptotic behavior of the wrapped process is also discussed in terms of circular Brownian motion. Besides, it is possible to derive a stochastic model for harmonic oscillators with random changes in direction and we give a diffusive approximation of this process. Furthermore, we introduce some extensions of the circular telegraph model in the asymmetric case and for non-Markovian waiting times as well. In this last case, we also provide some asymptotic results.

Keywords: Angular velocity; Circular brownian motion; Complex telegraph equation; Random harmonic oscillator; Semigroup operator; Wrapped probability distribution (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.07.001

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