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 theoryNature: Original
Retrieve article from Numdam
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 processesNature: Original Retrieve article from Numdam
XX: 04, 34-39, LNM 1204 (1986)
PONTIER, Monique;
STRICKER, Christophe;
SZPIRGLAS, Jacques
Sur le théorème de représentation par rapport à l'innovation Retrieve article from Numdam
XXI: 31, 534-543, LNM 1247 (1987)
PONTIER, Monique;
SZPIRGLAS, Jacques
Convergence des approximations de McShane d'une diffusion sur une variété compacte Retrieve article from Numdam
