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

 

Continuity properties of optimal stopping value


Author: John Elton
Journal: Proc. Amer. Math. Soc. 105 (1989), 736-746
MSC: Primary 60G40; Secondary 90C39
Erratum: Proc. Amer. Math. Soc. 107 (1989), 857.
MathSciNet review: 949876
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Abstract: The optimal stopping value of a sequence (finite or infinite) of integrable random variables is lower semicontinuous for the topology of convergence in distribution, when restricted to a collection with uniformly integrable negative parts. It is continuous for finite sequences which are adapted by a continuous invertible "triangular" function to independent sequences, such as partial averages; this is our main result. The proof depends on conditional weak convergence, uniform on compact sets, for such processes. A topological result on the inverses of triangular functions on iteratively connected domains may be of independent interest (§3).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0949876-5
PII: S 0002-9939(1989)0949876-5
Keywords: Optimal stopping value, weak convergence, conditional distribution, triangular function, adapted, iteratively connected
Article copyright: © Copyright 1989 American Mathematical Society