Hallo everybody,

does anyone know, if there exists a decomposition of the random variable such that

where

is measurable

are measurable

and are two algebras with

I just know the decomposition of stochastic processes (continuous in time), such that a (local) martingale remains a (local) martingale in the enlarged filtration (initial enlargement of filtration). The Doob-Meyer Decomposition doesn't work here either.

Thanks in advance!