Chaînes colorées: trois extensions d'une formule de P. Nelson

Abstract

Nelson [9], [10] has computed the generating function of return probabilities to the initial state for a particular Markov chain on permutations of three objects. The formula obtained is The present paper studies three distinct Markov chains generalizing the Nelson chain: the so-called three-coloured chain, with some birth-and-death processes on ℤ as a particular case, a chain on a graph close to the graph of the edges of a cube, and the daisy library. Two other themes piece together these chains: the notion of coloured chain and the technique of computation by additive processes.