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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60K05 Renewal theory
- 60J15 Random walks

**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*