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Random walks and periodic continued fractions

Published online by Cambridge University Press:  01 July 2016

Wolfgang Woess
Wolfgang Woess*
Affiliation:
Montanuniversität Leoben
*
∗Postal address: Institut für Mathematik und Angewandte Geometrie, Montanuniversität Leoben, A-8700 Leoben, Austria.
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Abstract

Nearest-neighbour random walks on the non-negative integers with transition probabilities p0,1 = 1, pk,k–1 = gk, pk,k+1 = 1– gk (0 < gk < 1, k = 1, 2, …) are studied by use of generating functions and continued fraction expansions. In particular, when (gk) is a periodic sequence, local limit theorems are proved and the harmonic functions are determined. These results are applied to simple random walks on certain trees.

Keywords

LOCAL LIMIT THEOREMHARMONIC FUNCTIONSIMPLE RANDOM WALK ON A TREESPHERICAL FUNCTION
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 1 , March 1985 , pp. 67 - 84
Copyright
Copyright © Applied Probability Trust 1985 

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