## The Annals of Mathematical Statistics

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

Lehner, G. One Dimensional Random Walk with a Partially Reflecting Barrier. Ann. Math. Statist. 34 (1963), no. 2, 405--412. doi:10.1214/aoms/1177704151. https://projecteuclid.org/euclid.aoms/1177704151