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Modern Stochastics: Theory and Applications


Probability distributions for the run-and-tumble models with variable speed and tumbling rate
Volume 6, Issue 1 (2019), pp. 3–12
Pub. online: 21 December 2018      Type: Research Article      Open accessOpen Access
Received
16 July 2018
Revised
8 November 2018
Accepted
7 December 2018
Published
21 December 2018

Abstract

In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed according to a non-stationary Poisson distribution with rate $\lambda (t)$. We show that, under suitable assumptions, we are able to find the exact form of the probability distribution. We also consider the space-fractional counterpart of this model, finding the characteristic function of the related process. A conclusive discussion is devoted to the potential applications to run-and-tumble models.

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Keywords
Telegraph equation with time-dependent velocity run-and-tumble models exact marginal probability distribution

MSC2010
60K35 60K99

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