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Correlated random walk

Published online by Cambridge University Press:  24 October 2008

J. Gillis
J. Gillis
Affiliation:
Weizmann Institute of ScienceIsrael Institute for Advanced StudyPrincetonNew Jersey
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Abstract

Random walk on a d-dimensional lattice is investigated such that, at any stage, the probabilities of the step being in the various possible directions depend upon the direction of the previous step. The motion may be characterized by a generating function which is here derived. The generating function is then used to obtain some general properties of the walk. Certain special cases are considered in greater detail. The existence of recurrent points is investigated in particular, and the probability of returning to the origin after 2n steps. This latter function is evaluated asymptotically for the cases d = 1 and d = an even integer.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 4 , October 1955 , pp. 639 - 651
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

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