The existence of regular conditional probabilities for Markov kernels

A.G. Nogales

Statistics & Probability Letters, 2013, vol. 83, issue 3, 891-897

Abstract: In this work, considering a Markov kernel (also called a stochastic kernel or transition probability) as a generalization of the concepts of the σ-field and the random variable, the concept of a conditional distribution (or regular conditional probability) of a Markov kernel given another is introduced. The existence of such a conditional distribution is proved under standard regularity conditions concerning the measurable spaces involved.

Keywords: Markov kernel; Regular conditional probability; Independence (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2012.12.008

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