Ito's lemma

Bazman · **Joined:** Mon, 29 Jan 2007 13:48:38 UTC **Posts:** 537

Hi there,

I need to apply Ito's lemma to:

$Y(t) = t^2X(t) -2\int_0^t sX(s) ds$

to determine if it is a martingale or not.

I am unsure about the 2nd term in particular.

Here is how I have tried to do it.

$\frac{\partial Y}{\partial t}=(2t X(t) -2 t X(t))dt$

so this part is zero.

$\frac{\partial Y}{\partial X(t)}= (t^2-2tX(t))dX-\frac{1}{2}*2*t*t$

so this part is non zero and therefore it is not a martingale.

in doing the second partial I have assumed that the derivative of the integral of the 2nd term wrt s is just the second term is this correct?

S.O.S. Mathematics CyberBoard

Ito's lemma

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