Séminaire Lotharingien de Combinatoire, B10h (1984), 3 pp.
[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 following version is available:
The paper has been finally published under the title
"Random walks and periodic continued fractions" in
Adv. in Appl. Probab. 17 (1985), 67-84.