Adapted probability distributions

Authors:
Douglas N. Hoover and H. Jerome Keisler

Journal:
Trans. Amer. Math. Soc. **286** (1984), 159-201

MSC:
Primary 60G05; Secondary 60E05

DOI:
https://doi.org/10.1090/S0002-9947-1984-0756035-8

MathSciNet review:
756035

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Abstract: We introduce a family of notions of equivalence for stochastic processes on spaces with an underlying filtration. These refine the notion of having the same distribution by taking account of the relation of the processes to their underlying filtrations. The weakest of these notions is the same as the notion of synonymity introduced by Aldous. Analysis of the strongest equivalence property leads to spaces with a strong universality property for adapted stochastic processes, which we call saturation. Spaces having this property contain 'strong' solutions to a large class of stochastic integral equations.

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DOI:
https://doi.org/10.1090/S0002-9947-1984-0756035-8

Article copyright:
© Copyright 1984
American Mathematical Society