Probability distributions for the run-and-tumble models with variable speed and tumbling rate
Open Access
- 21 December 2018
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 6 (1), 3-12
- https://doi.org/10.15559/18-vmsta127
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.Keywords
This publication has 28 references indexed in Scilit:
- Flying randomly in Rd with Dirichlet displacementsStochastic Processes and their Applications, 2012
- Light-powering Escherichia coli with proteorhodopsinProceedings of the National Academy of Sciences of the United States of America, 2007
- Time-fractional telegraph equations and telegraph processes with brownian timeProbability Theory and Related Fields, 2003
- THE SPACE-FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESSChinese Annals of Mathematics, Series B, 2003
- The generalized Cattaneo equation for the description of anomalous transport processesJournal of Physics A: General Physics, 1997
- Telegrapher’s equations with variable propagation speedsPhysical Review E, 1994
- Theory of continuum random walks and application to chemotaxisPhysical Review E, 1993
- Heat wavesReviews of Modern Physics, 1989
- A stochastic model related to the telegrapher's equationRocky Mountain Journal of Mathematics, 1974
- ON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON THE TELEGRAPH EQUATIONThe Quarterly Journal of Mechanics and Applied Mathematics, 1951