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arXiv · 2001.02487

Probability distributions for the run-and-tumble models with variable speed and tumbling rate

Luca Angelani·Roberto Garra
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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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Luca Angelani, Roberto Garra. 2020-01-08. Probability distributions for the run-and-tumble models with variable speed and tumbling rate. https://doi.org/10.15559/18-vmsta127

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