A rigorous definition of two-parameter point processes is given as a distribution of a denumerable number of random points in the plane. A characterization with stopping lines and relation with predictability are obtained. Using the one-parameter multivariate point-process representation, a general representation theorem for a wide class of martingales is presented, which extends the representation theorem with respect to a Poisson process.
Publié le : 1988-01-14
Classification:
Two-parameter point process,
stopping line,
martingale representation,
multivariate point process,
Poisson process,
predictable projection,
60G55,
60G48,
60G40,
60G60
@article{1176991900,
author = {Merzbach, Ely and Nualart, David},
title = {A Martingale Approach to Point Processes in the Plane},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 265-274},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991900}
}
Merzbach, Ely; Nualart, David. A Martingale Approach to Point Processes in the Plane. Ann. Probab., Tome 16 (1988) no. 4, pp. 265-274. http://gdmltest.u-ga.fr/item/1176991900/