Hallo!

There's a given probability space equipped with a filtration and a subfiltration .

And now I want to do a change of measure

, with

where

is an estimator for the unknown parameter which has a normal prior distribution

and is a brownian motion with respect to

are constants

I've also an explicit version of

is a brownian motion with respect to and is independent of

How can I now prove, that is a martingale?

I only know the Novikov condition,

.

But I think this condition isn't fulfilled.

Can anybody help me?

Thanks in advance!