On a Generalization of One Dimensional Random Walk with a Partially Reflecting Barrier

Abstract

Consider a one-dimensional random walk model where a particle starting at the origin at any instant either takes a jump through a unit distance to the right with probability p1, or stays at the same position with probability p0, or else takes a jump through either of 1, 2, … μ, units of distance to the left with probabilities p-1, p-2, …, p-μ respectively.