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A modified random walk in the presence of partially reflecting barriers

Published online by Cambridge University Press:  14 July 2016

Saroj Dua ,
Shobha Khadilkar  and
Kanwar Sen
Saroj Dua
Affiliation:
University of Delhi
Shobha Khadilkar
Affiliation:
University of Delhi
Kanwar Sen
Affiliation:
University of Delhi
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Abstract

The paper deals with the one-dimensional modified random walk in the presence of partially reflecting barriers at a and –b (a, b > 0). The simple one-dimensional random walk on a line is the motion-record of a particle which may extend over (–∞, + ∞) or be restricted to a portion of it by absorbing and/or reflecting barriers. Here we introduce the possibility of a particle staying put along with its moving a unit step to the right or to the left and find the bivariate generating functions of the probabilities of a particle reaching m (0 <m <a) under different conditions.

Keywords

MODIFIED RANDOM WALKPARTIALLY REFLECTING BARRIERSWAVEa-WAVEC-POINTSECTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 169 - 175
Copyright
Copyright © Applied Probability Trust 1976 

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References

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Lehner, G. (1963) One dimensional random walk with a partially reflecting barrier. Ann. Math. Statist. 34, 405–412.CrossRefGoogle Scholar