A characterization of adapted distribution. (English) Zbl 0634.60033

Author’s abstract: The notion of adapted distribution of a stochastic process was introduced in a recent paper of the author and H. J. Keisler [Trans. Am. Math. Soc. 286, 159-201 (1984; Zbl 0548.60019)]. Here we give a simple characterization of this notion in terms of filtration embeddability. This characterization allows us to show that for a local martingale M for which some ordinary stochastic differential equation \(X_ t=\int^{t}_{0}f(s,X_ s)dM_ s\) admits sufficient nonuniqueness in law of the solutions X, the class of possible joint laws of (M,X) determines the adapted law of M.
Reviewer: J.A.Goldstein


60G07 General theory of stochastic processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)


Zbl 0548.60019
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