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Some explicit results for an asymmetric two-dimensional random walk

Published online by Cambridge University Press:  24 October 2008

V. D. Barnett
V. D. Barnett
Affiliation:
Statistical Laboratory, University of Manchester
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Abstract

Three distinct methods are used to obtain exact expressions for various characteristics of a particular asymmetric two-dimensional random walk. The results obtained include, for the transient unrestricted walk, the probability of return to the starting-point and the average number of arrivals at the general lattice point; and, for a walk restricted within a rectangular absorbing barrier, the average number of arrivals at any accessible point and the absorption probabilities on the boundary. Whilst there is some duplication of results by using the three different methods of analysis, this is not extensive and provides a useful check on the results. Also the methods are of some general interest in themselves.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 451 - 462
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

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