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July 1998 Convergence of set valued sub- and supermartingales in the Kuratowski-Mosco sense
Shoumei Li, Yukio Ogura
Ann. Probab. 26(3): 1384-1402 (July 1998). DOI: 10.1214/aop/1022855757

Abstract

The purpose of this paper is to prove some convergence theorems of closed and convex set valued sub- and supermartingales in the Kuratowski–Mosco sense. To get submartingale convergence theorems, we give sufficient conditions for the Kudo–Aumann integral and Hiai–Umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables. We also give an example of a bounded closed convex set valued random variable whose Kudo–Aumann integral is not closed.

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Shoumei Li. Yukio Ogura. "Convergence of set valued sub- and supermartingales in the Kuratowski-Mosco sense." Ann. Probab. 26 (3) 1384 - 1402, July 1998. https://doi.org/10.1214/aop/1022855757

Information

Published: July 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0938.60031
MathSciNet: MR1640350
Digital Object Identifier: 10.1214/aop/1022855757

Subjects:
Primary: 28B20 , 60G42
Secondary: 60D05 , 60G48

Keywords: Kudo-Aumann integral , Kuratowski-Mosco convergence , Set valued submartingale , set valued supermartingale

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 3 • July 1998
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