Martin boundaries associated with a killed random walk

We start by studying the connection between the full Martin boundary associ ated 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 pro cess of weak increasing ladder heights and times in the random walk. We sho w that although the corresponding spatial boundaries are isomorphic, the sp ace time boundaries are not. The rest of the paper is devoted to determinin g these boundaries explicitly in the special case that the moment generatin g function of the step distribution exists in a non-empty interval. (C) 200 1 Editions scientifiques et medicales Elsevier SAS.