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

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.

Published at https://doi.org/10.15559/18-VMSTA127 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)

References in corpus (8)

• Lévy walks
• Dynamic density shaping of light driven bacteria
• Painting with bacteria: Smart templated self assembly using motile bacteria
• First-passage time of run-and-tumble particles
• Confined run-and-tumble swimmers in one dimension
• Dispersion relations for the time-fractional Cattaneo-Maxwell heat equation
• Random flights related to the Euler-Poisson-Darboux equation
• Random motions with space-varying velocities

Cited by in corpus (2)

• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Positing the problem of stationary distributions of active particles as third-order differential equation