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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 1211

Keywords: Enlargement of filtrations, Honest times

Nature: Original

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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

Comment: This result was independently discovered by Barlow,

Keywords: Enlargement of filtrations, Honest times

Nature: Original

Retrieve article from Numdam