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A correlated random walk model for two-dimensional diffusion

Published online by Cambridge University Press:  14 July 2016

Robin Henderson ,
Eric Renshaw  and
David Ford
Robin Henderson*
Affiliation:
British Nuclear Fuels Ltd
Eric Renshaw*
Affiliation:
University of Edinburgh
David Ford*
Affiliation:
Institute of Terrestrial Ecology
*
∗ Present address: Department of Statistics, University of Newcastle upon Tyne, Claremont Road, Newcastle upon Tyne NE1 7RU, U.K.
∗∗ Postal address: Department of Statistics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Rd, Edinburgh EH9 3JZ, U.K.
∗∗∗ Institute of Terrestrial Ecology, Bush Estate, Penicuik, Midlothian, EH26 0QB, U.K.
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Abstract

A two-dimensional lattice random walk is studied in which, at each stage, the direction of the next step is correlated to that of the previous step. An exact expression is obtained from the characteristic function for the dispersion matrix of the n-step transition probabilities, and the limiting diffusion equation is derived.

Keywords

LATTICEDISPERSIONCHARACTERISTIC FUNCTIONSPECTRAL DECOMPOSITION
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 2 , June 1984 , pp. 233 - 246
Copyright
Copyright © Applied Probability Trust 1984 

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