Continuity properties of optimal stopping value

Elton, John

doi:10.1090/S0002-9939-1989-0949876-5

Continuity properties of optimal stopping value
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by John Elton

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

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

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

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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