XI: 11, 120-131, LNM 581 (1977)
MEYER, Paul-André
Résultats récents de A. Benveniste en théorie des flots (Ergodic theory)
A filtered flow is said to be diffuse if there exists a r.v. ${\cal F}_0$-measurable $J$ such that given any ${\cal F}_0$-measurable r.v.'s $T$ and $H$, $P\{J\circ\theta_T=H, 0<T<\infty\}=0$. The main result of the paper is the fact that a diffuse flow contains all Lévy flows (flows of increments of Lévy processes, no invariant measure is involved). In particular, the Brownian flow contains a Poisson counter
Comment: This result on the whole line is similar to 1106, which concerns a half-line. The original paper of Benveniste appeared in Z. für W-theorie, 41, 1977/78
Keywords: Filtered flows, Poisson flow
Nature: Exposition
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