The Annals of Statistics

The Stochastic Processes of Borel Gambling and Dynamic Programming

David Blackwell

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Abstract

Associated with any Borel gambling model $G$ or dynamic programming model $D$ is a corresponding class of stochastic processes $M(G)$ or $M(D)$. Say that $G(D)$ is regular if there is a $D(G)$ with $M(D) = M(G)$. Necessary and sufficient conditions for regularity are given, and it is shown how to modify any model slightly to achieve regularity.

Article information

Source
Ann. Statist. Volume 4, Number 2 (1976), 370-374.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343412

Digital Object Identifier
doi:10.1214/aos/1176343412

Mathematical Reviews number (MathSciNet)
MR405557

Zentralblatt MATH identifier
0331.93055

JSTOR
links.jstor.org

Subjects
Primary: 49C15
Secondary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]

Keywords
Borel gambling dynamic programming

Citation

Blackwell, David. The Stochastic Processes of Borel Gambling and Dynamic Programming. Ann. Statist. 4 (1976), no. 2, 370--374. doi:10.1214/aos/1176343412. https://projecteuclid.org/euclid.aos/1176343412


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