XII: 09, 61-69, LNM 649 (1978)
YOR, Marc
Grossissement d'une filtration et semi-martingales~: théorèmes généraux (
General theory of processes)
Given a filtration $({\cal F}_t)$ and a positive random variable $L$, the so-called
progressively enlarged filtration is the smallest one $({\cal G}_t)$ containing $({\cal F}_t)$, and for which $L$ is a stopping time. The enlargement problem consists in describing the semimartingales $X$ of ${\cal F}$ which remain semimartingales in ${\cal G}$, and in computing their semimartingale characteristics. In this paper, it is proved that $X_tI_{\{t< L\}}$ is a semimartingale in full generality, and that $X_tI_{\{t\ge L\}}$ is a semimartingale whenever $L$ is
honest for $\cal F$, i.e., is the end of an $\cal F$-optional set
Comment: This result was independently discovered by Barlow,
Zeit. für W-theorie, 44, 1978, which also has a huge intersection with
1211. Complements are given in
1210, and an explicit decomposition formula for semimartingales in
1211Keywords: Enlargement of filtrations,
Honest timesNature: Original
Retrieve article from Numdam
XII: 10, 70-77, LNM 649 (1978)
DELLACHERIE, Claude;
MEYER, Paul-André
A propos du travail de Yor sur le grossissement des tribus (
General theory of processes)
This paper adds a few comments and complements to the preceding one
1209; for instance, the enlargement map is bounded in $H^1$
Keywords: Enlargement of filtrations,
Honest timesNature: Original Retrieve article from Numdam
XII: 11, 78-97, LNM 649 (1978)
JEULIN, Thierry;
YOR, Marc
Grossissement d'une filtration et semi-martingales~: Formules explicites (
General theory of processes)
This contains very substantial improvements on
1209, namely, the explicit computation of the characteristics of the semimartingales involved
Comment: For additional results on enlargements, see the two Lecture Notes volumes
833 (T. Jeulin) and
1118. See also
1350Keywords: Enlargement of filtrations,
Honest timesNature: Original Retrieve article from Numdam
XII: 40, 515-522, LNM 649 (1978)
DELLACHERIE, Claude
Supports optionnels et prévisibles d'une P-mesure et applications (
General theory of processes)
A $P$-measure is a measure on $\Omega\times
R_+$ 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 timesNature: Original Retrieve article from Numdam
