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Martin boundaries associated with a killed random walk
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Alili, Larbi and Doney, R. A. (2001) Martin boundaries associated with a killed random walk. Annales de l'Institut Henri Poincare (B) Probability and Statistics, Volume 37 (Number 3). pp. 313-338. doi:10.1016/S0246-0203(00)01069-4 ISSN 0246-0203.
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Official URL: http://dx.doi.org/10.1016/S0246-0203(00)01069-4
Abstract
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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Journal or Publication Title: | Annales de l'Institut Henri Poincare (B) Probability and Statistics | ||||
| Publisher: | Institute of Mathematical Statistics | ||||
| ISSN: | 0246-0203 | ||||
| Official Date: | May 2001 | ||||
| Dates: |
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| Volume: | Volume 37 | ||||
| Number: | Number 3 | ||||
| Number of Pages: | 25 | ||||
| Page Range: | pp. 313-338 | ||||
| DOI: | 10.1016/S0246-0203(00)01069-4 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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