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
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