We prove that in continuous time, the extremal elements of the set of adapted random measures on $\mathbb{R}^2_+$ are Dirac measures, assuming the underlying filtration satisfies the conditional qualitative independence property. This result is deduced from a theorem in discrete time which provides a correspondence between adapted random measures on $\mathbb{N}^2$ and two-parameter randomized stopping points in the sense of Baxter and Chacon. As an application we show the existence of optimal stopping points for upper semicontinuous two-parameter processes in continuous time.
Publié le : 1992-04-14
Classification:
Optimal stopping,
two-parameter processes,
randomized stopping point,
60G40,
60G57
@article{1176989810,
author = {Nualart, David},
title = {Randomized Stopping Points and Optimal Stopping on the Plane},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 883-900},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989810}
}
Nualart, David. Randomized Stopping Points and Optimal Stopping on the Plane. Ann. Probab., Tome 20 (1992) no. 4, pp. 883-900. http://gdmltest.u-ga.fr/item/1176989810/