[944] Correction

[Gautam Iyer]

Hi All,

When computing the joint quadratic variation of Itô integrals, I quickly
said in class that it follows from the "4ab trick". This isn't true, and
some of you pointed it out to me yesterday.

Accordingly, I updated the notes to include a proof sketch. (The idea is
to look at sums of the product of the increments and approximate it.)

Also, another omission in the notes was biliniarity of the joint
quadratic variation: I never said in class that

    [X, Y+Z] = [X,Y] + [X, Z].

The proof of this *doesn't* follow from the 4ab trick, and requires the
martingale characterization. If you are curious about the proof, I wrote
this up also and it is now Proposition 9.9 in the notes. (Thanks for
pointing out the omission to me yesterday.)

Review problems: I put 4 up at the very end of the notes. I will put up
a few more tonight, and do some subset of them in class tomorrow.

GI

-- 
Alternative definitions of terms from Math Lectures:
QUANTIFY: I can't find anything wrong with your proof except that it
won't work if x is a moon of Jupiter (Popular in applied math courses).