Abstract
In the present paper we consider the one dimensional random walk of a particle restricted by a partially reflecting barrier. The reflecting barrier is described by a coefficient of reflection $r$. The probability of finding a particle at a lattice point $m$ after $N$ steps is calculated and expressed in terms of hypergeometric functions of the $_2F_1$-type. Other theorems are deduced concerning the one dimensional random walk. For instance the number of paths leading from one lattice point to another lattice point in $N$ steps and showing a given number of reflections at the barrier is calculated.
Citation
G. Lehner. "One Dimensional Random Walk with a Partially Reflecting Barrier." Ann. Math. Statist. 34 (2) 405 - 412, June, 1963. https://doi.org/10.1214/aoms/1177704151
Information