Time Reversions of Markov Processes

A time reversion of a Markov process was discussed by Kolmogoroff for Markov chains in 1936 [6] and for a diffusion in 1937 [7l He described it as a process having an adjoint transition probability. Although his treatment is purely analytical, in his case if the process xt has an invariant distribut...

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Bibliographic Details
Published in:Nagoya mathematical journal 1964-06, Vol.24, p.177-204
Main Author: Nagasawa, Masao
Format: Article
Language:English
Subjects:
60.60
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Summary:A time reversion of a Markov process was discussed by Kolmogoroff for Markov chains in 1936 [6] and for a diffusion in 1937 [7l He described it as a process having an adjoint transition probability. Although his treatment is purely analytical, in his case if the process xt has an invariant distribution, the reversed process zt = x-t is the process with the adjoint transition probability. In this discussion, however, it is very restrictive that the initial distribution of the process must be an invariant measure.
ISSN:0027-7630
2152-6842
DOI:10.1017/S0027763000011405