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June, 1963 One Dimensional Random Walk with a Partially Reflecting Barrier
G. Lehner
Ann. Math. Statist. 34(2): 405-412 (June, 1963). DOI: 10.1214/aoms/1177704151


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.


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G. Lehner. "One Dimensional Random Walk with a Partially Reflecting Barrier." Ann. Math. Statist. 34 (2) 405 - 412, June, 1963.


Published: June, 1963
First available in Project Euclid: 27 April 2007

zbMATH: 0108.31201
MathSciNet: MR146899
Digital Object Identifier: 10.1214/aoms/1177704151

Rights: Copyright © 1963 Institute of Mathematical Statistics

Vol.34 • No. 2 • June, 1963
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