On the Expected Number of Visits of a Particle before Absorption in a Correlated Random Walk

Abstract

Let a particle move along a straight line a unit distance during every interval of time τ. During the first interval τ it moves to the right with probability ρ1 and to the left with probability ρ2 = 1 - ρ1. Thereafter at the end of each interval τ, the particle with probability p continues its motion in the same direction as in the previous step and with probability q = l - p reverses it.