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Zbl 0981.60083
Alili, L.; Doney, R.A.
Martin boundaries associated with a killed random walk. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 37, No.3, 313-338 (2001). ISSN 0246-0203

In the first part of the paper there are studied 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. Then, it is shown that although the corresponding spatial boundaries are isomorphic, the space time boundaries are not. The rest of the paper is devoted to determine these boundaries explicitly in the special case that the moment generating function of the step distribution exists in a non-empty interval.
[Valentin Topchii (Omsk)]

MSC 2000:: *60K05 Renewal theory
60G50 Sums of independent random variables

Keywords: random walk; bivariate renewal process; Martin boundary

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