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XIV: 23, 205-208, LNM 784 (1980)
SEYNOU, Aboubakary
Sur la compatibilité temporelle d'une tribu et d'une filtration discrète (General theory of processes)
Let us say that a $\sigma$-field ${\cal G}$ is embedded into a filtration $({\cal H}_n)$ if ${\cal G}= {\cal H}_T$ for some ${\cal H}$-stopping time $T$, that a filtration $({\cal F}_n)$ is embedded into $({\cal H}_n)$ if ${\cal F}_S$ can be embedded into $({\cal H}_n)$ for every ${\cal F}$-stopping time $S$, and finally that ${\cal G}$ and ${\cal F}$ or $({\cal F}_n)$ are compatible if they can be embedded into one single filtration $({\cal H}_n)$. Then the question investigated is whether the compatibility of ${\cal G}$ and the individual $\sigma$-fields ${\cal F}_n$ implies that of ${\cal G}$ and the whole filtration $({\cal F}_n)$
Comment: This problem arose from the spectral point of view on stochastic integration as in 1123
Keywords: Filtrations
Nature: Original
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