The Annals of Mathematical Statistics

One Dimensional Random Walk with a Partially Reflecting Barrier

G. Lehner

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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


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