Random motion with gamma-distributed alternating velocities in biological modeling

TL;DR

This paper studies a generalized telegraph process with gamma-distributed switching times, providing analytical expressions for its probability law and mean, motivated by biological applications involving microorganism movement.

Contribution

It introduces a novel model of alternating motion with gamma-distributed switching times, extending previous telegraph process models in biological contexts.

Findings

Derived the probability law of the process

Calculated the mean of the process

Applicable to modeling microorganism movement

Abstract

Motivated by applications in mathematical biology concerning randomly alternating motion of micro-organisms, we analyze a generalized integrated telegraph process. The random times between consecutive velocity reversals are gamma-distributed, and perform an alternating renewal process. We obtain the probability law and the mean of the process.