Martin boundaries associated with a killed random walk

We start by studying the connection between the full Martin boundary associated with a space time version of a random walk which is killed on entering the negative half-line, and that associated with the bivariate renewal process of weak increasing ladder heights and times in the random walk. We show that although the corresponding spatial boundaries are isomorphic, the space time boundaries are not. The rest of the paper is devoted to determining these boundaries explicitly in the special case that the moment generating function of the step distribution exists in a non-empty interval. (C) 2001 Editions scientifiques et medicales Elsevier SAS.