Telegraph Evolutions in Inhomogeneous Media

#### N. Ratanov

1999, v.5, №1, 53-68

ABSTRACT

We consider a random walk on a line with abrupt changes in velocity directions at Poisson times. It is known due to M. Kac (1959) that the probability distribution of this motion fits in the so-called telegraph equation. We generalize this observation to the case of motions in inhomogeneous and in anisotropic media. The probabilities related to such motions with reflectors and traps are calculated as the solutions of boundary value problems for telegraph equation.

Keywords: random evolutions,Poisson process,telegraph equation,diffusionapproximation