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The transient behaviour of the simple random walk in the plane

Published online by Cambridge University Press:  14 July 2016

D. Y. Downham  and
S. B. Fotopoulos
D. Y. Downham*
Affiliation:
University of Liverpool
S. B. Fotopoulos*
Affiliation:
Washington State University
*
∗ Currently at the Department of Mathematics and Computing, Sultan Qaboos University, P.O. Box 324 86 Al-Khod, Muscat, Sultanate of Oman.
∗∗ Postal address: Department of Management and Systems, Washington State University, Pullman, WA 99164, USA.
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Abstract

For the simple two-dimensional random walk on the vertices of a rectangular lattice, the asymptotic forms of several properties are well known, but their forms can be insufficiently accurate to describe the transient process. Inequalities with the correct asymptotic form are derived for six such properties. The rates of approach to the asymptotic form are derived. The accuracy of the bounds and some practical implications of the results are discussed.

Keywords

INEQUALITIESTUMOUR GROWTH
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 58 - 69
Copyright
Copyright © Applied Probability Trust 1988 

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References

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