## The Annals of Mathematical Statistics

### One Dimensional Random Walk with a Partially Reflecting Barrier

G. Lehner

#### 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.

#### Article information

Source
Ann. Math. Statist., Volume 34, Number 2 (1963), 405-412.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177704151

Digital Object Identifier
doi:10.1214/aoms/1177704151

Mathematical Reviews number (MathSciNet)
MR146899

Zentralblatt MATH identifier
0108.31201

JSTOR