Persistent random walk

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.