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April, 1992 Randomized Stopping Points and Optimal Stopping on the Plane
David Nualart
Ann. Probab. 20(2): 883-900 (April, 1992). DOI: 10.1214/aop/1176989810


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.


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David Nualart. "Randomized Stopping Points and Optimal Stopping on the Plane." Ann. Probab. 20 (2) 883 - 900, April, 1992.


Published: April, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0758.60042
MathSciNet: MR1159578
Digital Object Identifier: 10.1214/aop/1176989810

Primary: 60G40
Secondary: 60G57

Keywords: Optimal stopping , randomized stopping point , two-parameter processes

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 2 • April, 1992
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