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A two-dimensional random walk in the presence of a partially reflecting barrier

Published online by Cambridge University Press:  14 July 2016

Noel Cressie
Noel Cressie*
Affiliation:
Australian National University
*
*Now at Princeton University
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Abstract

A general two-dimensional random walk is considered with a barrier along the y-axis. Absorption probabilities are derived when the barrier is absorbing, and when it is semi-reflecting.

Keywords

IMBEDDED ONE-DIMENSIONAL RANDOM WALKULTIMATE ABSORPTION PROBABILITIES
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 199 - 205
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Barnett, V. D. (1963) Some explicit results for an asymmetric two-dimensional random walk Proc. Camb. Phil. Soc. 59, 451–462.Google Scholar
[2] Barnett, V. D. (1965) Wald's identity and absorption probabilities for two-dimensional random walks Proc. Camb. Phil. Soc. 61, 747–762.Google Scholar
[3] Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar
[4] Mccrea, W. H. and Whipple, F. J. W. (1940) Random paths in two and three dimensions Proc. Roy. Soc. Edinburgh Sect. A 60, 281–298.CrossRefGoogle Scholar