Quick search | Browse volumes | |

IX: 25, 466-470, LNM 465 (1975)

**MEYER, Paul-André**; **YAN, Jia-An**

Génération d'une famille de tribus par un processus croissant (General theory of processes)

The previsible and optional $\sigma$-fields of a filtration $({\cal F}_t)$ on $\Omega$ are studied without the usual hypotheses: no measure is involved, and the filtration is not right continuous. It is proved that if the $\sigma$-fields ${\cal F}_{t-}$ are separable, then so is the previsible $\sigma$-field, and the filtration is the natural one for a continuous strictly increasing process. A similar result is proved for the optional $\sigma$-field assuming $\Omega$ is a Blackwell space, and then every measurable adapted process is optional

Comment: Making the filtration right continuous generally destroys the separability of the optional $\sigma$-field

Keywords: Previsible processes, Optional processes

Nature: Original

Retrieve article from Numdam

Génération d'une famille de tribus par un processus croissant (General theory of processes)

The previsible and optional $\sigma$-fields of a filtration $({\cal F}_t)$ on $\Omega$ are studied without the usual hypotheses: no measure is involved, and the filtration is not right continuous. It is proved that if the $\sigma$-fields ${\cal F}_{t-}$ are separable, then so is the previsible $\sigma$-field, and the filtration is the natural one for a continuous strictly increasing process. A similar result is proved for the optional $\sigma$-field assuming $\Omega$ is a Blackwell space, and then every measurable adapted process is optional

Comment: Making the filtration right continuous generally destroys the separability of the optional $\sigma$-field

Keywords: Previsible processes, Optional processes

Nature: Original

Retrieve article from Numdam