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4 matches found
XIII: 32, 378-384, LNM 721 (1979)
SZPIRGLAS, Jacques; MAZZIOTTO, Gérald
Théorème de séparation dans le problème d'arrêt optimal (General theory of processes)
Let $({\cal G}_t)$ be an enlargement of a filtration $({\cal F}_t)$ with the property that for every $t$, if $X$ is ${\cal G}_t$-measurable, then $E[X\,|\,{\cal F}_t]=E[X\,|\,{\cal F}_\infty]$. Then if $(X_t)$ is a ${\cal F}$-optional process, its Snell envelope is the same in both filtrations. Applications are given to filtering theory
Keywords: Optimal stopping, Snell's envelope, Filtering theory
Nature: Original
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XV: 48, 673-688, LNM 850 (1981)
MAZZIOTTO, Gérald; SZPIRGLAS, Jacques
Un exemple de processus à deux indices sans l'hypothèse F4 (Several parameter processes)
A natural two-parameter filtration is associated with a random point in the positive quadrant $R^2_+$. Though it does not satisfy in general the Cairoli-Walsh commutation property called F4, it is possible to develop for this filtration a reasonable theory of optional and previsible processes, projection theorems, etc
Keywords: Two-parameter processes
Nature: Original
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XVII: 40, 418-424, LNM 986 (1983)
MAZZIOTTO, Gérald
Régularité à droite des surmartingales à deux indices et théorème d'arrêt
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XX: 09, 81-94, LNM 1204 (1986)
MAZZIOTTO, Gérald; MILLET, Annie
Points, lignes et systèmes d'arrêt flous et problème d'arrêt optimal
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