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Kolmogorov Extension, Martingale Convergence, and Compositionality of Processes

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Abstract

We show that the Kolmogorov extension theorem and the Doob martingale convergence theorem are two aspects of a common generalization, namely a colimit-like construction in a category of Radon spaces and reversible Markov kernels. The construction provides a compositional denotational semantics for standard iteration operators in programming languages, e.g. Kleene star or while loops, as a limit of finite approximants, even in the absence of a natural partial order.

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2015-12-30

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Kolmogorov Extension; Martingale Convergence; Markov Process; Probabilistic Programs

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technical report

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