[944] Fix of mistake from today

[Gautam Iyer]

Hi All,

The direct conditioning argument I gave in class today (showing that MN
is a martingale if M and N are independent martingales) is wrong. The
cross term DOES NOT go away. I suspect that when I wrote the notes I
fell for the trick  and said

    E( XY | F) = E(X | F) E(Y | F)

if X and Y are independent. This is of course false, as I said today
(and had already explicitly said in the notes).

The fix required a direct calculation using the limit definition of the
joint quadratic variation, and I wrote it up in Proposition 9.10 right
now. Take a look when you get a chance.

I will ask Ryan to go over it in recitation as well.

GI

-- 
Little Johnny was a scientist. Little Johnny is no more. For what he
thought was H2O was H2SO4.