Random walks in an inhomogeneous one-dimensional medium with reflecting and absorbing barriers

Abstract

It is considered a particle that moves in an inhomogeneous one-dimensional medium. Its velocity changes direction in Poisson times. For such a random process, the Kolmogorov equations are derived backwards and forwards. The explicit formulas for the probability distributions of this process are obtained, as well as the formulas for similar processes in the presence of reflective and absorbent barriers.