Continuity properties of optimal stopping value

Author:
John Elton

Journal:
Proc. Amer. Math. Soc. **105** (1989), 736-746

MSC:
Primary 60G40; Secondary 90C39

DOI:
https://doi.org/10.1090/S0002-9939-1989-0949876-5

Erratum:
Proc. Amer. Math. Soc. **107** (1989), 857.

MathSciNet review:
949876

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0949876-5

Keywords:
Optimal stopping value,
weak convergence,
conditional distribution,
triangular function,
adapted,
iteratively connected

Article copyright:
© Copyright 1989
American Mathematical Society