Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Martin boundaries associated with a killed random walk


Code(s) de Classification MSC:

Résumé: First we study a mapping between the full space-time Martin boundary of a random walk killed on becoming negative, and the full martin boundary of the bivariate renewal process of ladder heights and times of the random walk. We show that although the corresponding spatial boundaries have been shown to be isomorphic, this is not the case for the space-time boundaries. The remainder of the paper is devoted to finding these boundaries explicitly in the special case that the moment-generating function of the step-distribution exists on a non-empty interval.

Mots Clés: Random walk ; killed random walk ; Martin boundary ; ladder processes, Green's functions

Date: 2000-03-31

Prépublication numéro: PMA-583