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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On representation and regularity of continuous parameter multivalued martingales


Authors: Dong Wenlong and Wang Zhenpeng
Journal: Proc. Amer. Math. Soc. 126 (1998), 1799-1810
MSC (1991): Primary 60D05, 60G25, 60G35, 60G48
MathSciNet review: 1485468
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Abstract: In this paper we study multivalued martingales in continuous time. First we show that every multivalued martingale in continuous time can be represented as the closure of a sequence of martingale selections. Then we prove two results concerning the cadlag modifications of continuous time multivalued martingales, in Kuratowski-Mosco convergence and in convergence in the Hausdorff metric respectively.


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Additional Information

Dong Wenlong
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
Email: wdong@scf.usc.edu

Wang Zhenpeng
Affiliation: Department of Mathematical Statistics, East China Normal University, Shanghai 200062, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04726-1
PII: S 0002-9939(98)04726-1
Keywords: Cadlag modification, continuous parameter multivalued martingales, Kuratowski-Mosco convergence, martingale selections, right-closed martingales
Received by editor(s): May 4, 1995
Received by editor(s) in revised form: May 12, 1996
Communicated by: Richard T. Durrett
Article copyright: © Copyright 1998 American Mathematical Society