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: Stopping Nature: Original Retrieve article from NumdamXXI: 34, 574-578, LNM 1247 (1987) DUDLEY, Richard M.; STROOCK, Daniel W. Slepian's inequality and commuting semigroups Retrieve article from Numdam
Retrieve article from Numdam