1. State and prove the two-dimensional Itô formula. 2. Prove that if Xt , Yt are two Itô processes of the form (9.9), then d ( XtYt )= XtdYt + YtdXt + dXtdYt , where in the last term the same rules...

1.
State and prove the two-dimensional Itô formula.

2.
Prove that if
Xt,
Yt
are two Itô processes of the form (9.9), then

d(XtYt)=
XtdYt
+
YtdXt
+
dXtdYt
,

where in the last term the same rules apply as in the Itô formula.

3.
Calculate

∫t0sdBs
.

Hint: Apply Itô lemma to
Xt
=
Bt
and
f
(t
,

x) =
tx.