The persistent random walk is a modification of the

random walk In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space. An elementary example of a rand ...

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^/\tau

, then the population density

n

evolves according to

(2\tau^ \partial_t  + \partial_ - c_0^2 \partial_) n = 0

which is the

telegrapher's equation The telegrapher's equations (or telegraph equations) are a set of two coupled, linear partial differential equations that model voltage and Electric current, current along a linear electrical transmission line. The equations are important because ...

References

{{Reflist Stochastic processes Variants of random walks