The Annals of Probability

Notes on Constructive Probability Theory

Y. K. Chan

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Abstract

This paper is part of the constructive program, initiated by E. Bishop, of systematic examination of classical mathematics for their computational content. From this constructive standpoint, basic concepts in probability theory are studied. Positive proofs are then given to some important theorems: Ionescu-Tulcea's theorem, a submartingale convergence theorem, and the construction of a Markov process from a strongly continuous semi-group of transition operators.

Article information

Source
Ann. Probab., Volume 2, Number 1 (1974), 51-75.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996751

Digital Object Identifier
doi:10.1214/aop/1176996751

Mathematical Reviews number (MathSciNet)
MR356198

Zentralblatt MATH identifier
0278.60045

JSTOR
links.jstor.org

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G45 02E99

Keywords
Constructive analysis construction of Markov processes sample regularity of Markov processes with strongly continuous semi-groups convergence of submartingales.

Citation

Chan, Y. K. Notes on Constructive Probability Theory. Ann. Probab. 2 (1974), no. 1, 51--75. doi:10.1214/aop/1176996751. https://projecteuclid.org/euclid.aop/1176996751


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