Persistent random walk

Short description: Modification of the random walk model

The persistent random walk is a modification of the random walk model.

A population of particles are distributed on a line, with constant speed $c_0$, and each particle's velocity may be reversed at any moment. The reversal time is exponentially distributed as $e^{-t/\tau }/\tau$, then the population density $n$ evolves according to$$(2{\tau }^{-1}{\partial }_t+{\partial }_{tt}-c_0^2{\partial }_{xx})n=0$$which is the telegrapher's equation.