Trinomial random walk with one or two imperfect absorbing barriers

Abstract

Abstract Trinomial random walk, with one or two barriers, on the non-negative integers is discussed. At the barriers, the particle is either annihilated or reflects back to the system with respective probabilities 1 − ρ, ρ at the origin and 1 − ω, ω at L, 0 ≤ ρ,ω ≤ 1. Theoretical formulae are given for the probability distribution, its generating function as well as the mean of the time taken before absorption. In the one-boundary case, very qualitatively different asymptotic forms for the result, depending on the relationship between transition probabilities and the annihilation probability, are obtained.