Generating function for the first passage characteristics of evanescent run-and-tumble particles

Abstract

We formulate the evolution equations for a confined, one-dimensional, exponentially evanescent run-and-tumble particles model, and calculate the generating function for first passage characteristics. We obtain modified telegrapher’s equations for the evolution of the probability current and the probability density function of the run-and-tumble particles. The generating function can be used to calculate the eventual absorption probability at a point, and moments of the conditional first passage probability density.