dc.contributor.author | Merzbach, Ely | |
dc.contributor.author | Nualart, David | |
dc.date.accessioned | 2015-03-12T16:37:36Z | |
dc.date.available | 2015-03-12T16:37:36Z | |
dc.date.issued | 1986-02-06 | |
dc.identifier.citation | Merzbach, Ely; Nualart, David. A Characterization of the Spatial Poisson Process and Changing Time. Ann. Probab. 14 (1986), no. 4, 1380--1390. http://dx.doi.org/10.1214/aop/1176992378. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/17066 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176992378. | en_US |
dc.description.abstract | Watanabe proved that if Xt is a point process such that Xt−t is a martingale, then Xt is a Poisson process and this result was generalized by Bremaud for doubly stochastic Poisson processes. Here we define two-parameter point processes and extend this property without needing the strong martingale condition. Using this characterization, we study the problem of transforming a two-parameter point process into a two-parameter Poisson process by means of a family of stopping lines as a time change. Nualart and Sanz gave conditions in order to transform a square integrable strong martingale into a Wiener process. Here, we do the same for the Poisson process by a similar method but under more general conditions. | en_US |
dc.publisher | Institute of Mathematical Statistics (IMS) | en_US |
dc.subject | point process | en_US |
dc.subject | poisson | en_US |
dc.subject | two-parameter processes | en_US |
dc.subject | martingale | en_US |
dc.subject | intensity | en_US |
dc.subject | changing time | en_US |
dc.subject | stopping line | en_US |
dc.title | A Characterization of the Spatial Poisson Process and Changing Time | en_US |
dc.type | Article | |
kusw.kuauthor | Nualart, David | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1214/aop/1176992378 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item does not meet KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess | |