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Lattice-valued random walks with Markov chain dependent steps

Published online by Cambridge University Press:  24 October 2008

D. J. Daley
D. J. Daley
Affiliation:
Statistics Department (IAS), The Australian National University
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Abstract

The probability of ever returning to the origin and the mean square displacement after n steps are studied for some lattice-valued random walks, whose successive steps constitute a Markov chain on a finite state space with transition probabilities of a simple kind, and such that the returns to the origin form a regenerative phenomenon. The case of walks on a diamond lattice with no immediate reversals is included: this example is relevant as a polymer chain building model. The numerical evaluation of the return probabilities of some three-dimensional walks is discussed and examples given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 1 , July 1979 , pp. 115 - 126
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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