Séminaire Lotharingien de Combinatoire, B10h (1984).
[Formerly: Publ. I.R.M.A. Strasbourg, 1987, 340/S-10, p.
105-108.]
Wolfgang Woess
Einfache Irrfahrten auf radialen Bämen
Abstract.
Nearest-neighbour random walks on the nonnegative integers with
transition probabilities p0,1=1,
pk,k-1=g
k, pk,k+1=1-gk
(0<gk<1, k=1,2,...) are studied
using 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.
The paper has been finally published under the title
"Random walks and periodic continued fractions" in
Adv. in Appl. Probab. 17 (1985), 67-84.