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6 matches found
VI: 02, 35-50, LNM 258 (1972)
AZÉMA, Jacques
Une remarque sur les temps de retour. Trois applications (Markov processes, General theory of processes)
This paper is the first step in the investigations of Azéma on the ``dual'' form of the general theory of processes (for which see Azéma (Ann. Sci. ENS, 6, 1973, and 814). Here the $\sigma$-fields of cooptional and coprevisible sets are introduced in a Markovian set-up, and without their definitive names. A section theorem by return times is proved, and applications to the theory of Markov processes are given
Keywords: Homogeneous processes, Coprevisible processes, Cooptional processes, Section theorems, Projection theorems, Time reversal
Nature: Original
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IX: 08, 239-245, LNM 465 (1975)
DELLACHERIE, Claude; MEYER, Paul-André
Un nouveau théorème de projection et de section (General theory of processes)
Optional section and projection theorems are proved without assuming the ``usual conditions'' on the filtration
Comment: This paper is obsolete. As stated at the end by the authors, the result could have been deduced from the general theorem in Dellacherie 705. The result takes its definitive form in Dellacherie-Meyer, Probabilités et Potentiel, theorems IV.84 of vol. A and App.1, \no~6
Keywords: Section theorems, Optional processes, Projection theorems
Nature: Original
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XI: 02, 21-26, LNM 581 (1977)
Application d'un théorème de G. Mokobodzki à la théorie des flots (Ergodic theory, General theory of processes)
The purpose of this paper is to extend to the theory of filtered flows (for which see 901 and 902) the dual version of the general theory of processes due to Azéma (for which see 814 and 937), in particular the association with any measurable process of suitable projections which are homogeneous processes. An important difference here is the fact that the time set is the whole line. Here the class of measurable processes which can be projected is reduced to a (not very explicit) class, and a commutation theorem similar to Azéma's is proved. The proof uses the technique of medial limits due to Mokobodzki (see 719), which in fact was developed precisely at the author's request to solve this problem
Keywords: Filtered flows, Stationary processes, Projection theorems, Medial limits
Nature: Original
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XII: 40, 515-522, LNM 649 (1978)
Supports optionnels et prévisibles d'une P-mesure et applications (General theory of processes)
A $P$-measure is a measure on $\Omega\timesR_+$ which does not charge $P$-evanescent sets. A $P$-measure has optional and previsible projections which are themselves $P$-measures. As usual, supports are minimal sets carrying a measure, possessing different properties like being optional/previsible, being right/left closed. The purpose of the paper is to find out which kind of supports do exist. Applications are given to honest times
Comment: See 1339 for a complement concerning honest times
Keywords: Projection theorems, Support, Honest times
Nature: Original
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XIV: 11, 112-115, LNM 784 (1980)
STRICKER, Christophe
Projection optionnelle des semi-martingales (Stochastic calculus)
Let $({\cal G}_t)$ be a subfiltration of $({\cal F}_t)$. Since the optional projection on $({\cal G}_t)$ of a ${\cal F}$-martingale is a ${\cal G}$-martingale, and the projection of an increasing process a ${\cal G}$-submartingale, projections of ${\cal F}$-semimartingales ``should be'' ${\cal G}$-semimartingales. This is true for quasimartingales, but false in general
Comment: The main results on subfiltrations are proved by Stricker in Zeit. für W-Theorie, 39, 1977
Keywords: Semimartingales, Projection theorems
Nature: Original
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XIV: 49, 500-546, LNM 784 (1980)
Tribus de Meyer et théorie des processus (General theory of processes, Stochastic calculus)
The subject of this paper is the study of the $\sigma$-field on $R_+\times\Omega$ generated by a family of cadlag processes including the deterministic ones, and stable under stopping at non-random times. Of course the optional and previsible $\sigma$-fields are Meyer $\sigma$-fields in this very general sense. It is a matter of wonder to see how far one can go with such simple hypotheses, which were suggested by Dellacherie 705
Comment: This beautiful paper was generally ignored. If a suggestive name had been used instead of the terminology ``Meyer $\sigma$-field'', its fate might have been different. See 1524 for an interesting application. The work of Fourati (partly unpublished) follows along the same lines, but including time reversal: see 2119
Keywords: Projection theorems, Section theorems
Nature: Original
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