Trinomial random walk with one or two imperfect absorbing barriers

Year, pages: 2008, 353 - 376

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.

El-Shehawey, M. 2008. Trinomial random walk with one or two imperfect absorbing barriers. In Mathematica Slovaca, vol. 58, no.3, pp. 353-376. 0139-9918.

El-Shehawey, M. (2008). Trinomial random walk with one or two imperfect absorbing barriers. Mathematica Slovaca, 58(3), 353-376. 0139-9918.