Random walks and periodic continued fractions
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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.
1985 ◽
Vol 17
(01)
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pp. 67-84
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2011 ◽
Vol 16
(0)
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pp. 1-44
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2019 ◽
Vol 176
(1-2)
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pp. 669-735
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2005 ◽
Vol 15
(1)
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pp. 35-82
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