PREDICTABLE EXTENSIONS OF GIVEN FILTRATIONS
Abstract: Filtrations with the property that every stopping time is predictable are of
some importance in stochastic analysis, especially in connection with the Girsanov
transformation (cf. e.g. Chung and Williams [1]). Presumably for that reason, S.
Kwapień stated the problem whether any given filtration can be extended (in a sense
defined below) to a filtration for which every stopping time is predictable. In this
paper, this problem of Kwapień is solved positively: Any filtration has a predictable
extension.
The extension we construct has even the stronger property: any square integrable
martingale is a stochastic integral process relative to a certain Brownian motion.
1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -