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.