XI: 06, 51-58, LNM 581 (1977)
DUDLEY, Richard M.;
GUTMANN, Sam
Stopping times with given laws (
General theory of processes)
Given a filtration ${\cal A}_t$ such that for all $t>0$ the law $P$ restricted to ${\cal A}_t$ is non-atomic, then for every law $\mu$ on the half-line there exists a stopping time with law $\mu$. The proof uses an interesting measure theoretic lemma on decreasing sequences of non-atomic $\sigma$-fields
Comment: It follows that the Brownian filtration contains a process whose law is that of a Poisson process (though of course it is not a Poisson process
of the Brownian filtration )
Keywords: StoppingNature: Original
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