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A problem I have here. I am trying to solve a problem involving Ito Integrals and Riemann interals.

## Homework Statement

Prove

[tex]\int^{T}_{0} tdW(t) = TW(T) -\int^{T}_{0} W(t)dt [/tex]

## Homework Equations

I want to solve this question

**WITHOUT**using Ito's Lemma directly.

## The Attempt at a Solution

OK I know that in general, the Ito integral and the Riemann integral are going to be slightly different. The Ito Integral will have an extra term.

So in my question, I know if I was to generally just integrate the Riemann integral, I would get:

[tex]\int^{T}_{0} tdW(t) = TW(T) [/tex]

But I know the Ito integral adds the extra:

[tex] -\int^{T}_{0} W(t)dt [/tex]

But how does this arise? Is it possible to show how using

**the mean square error**? I keep reading the mean square error when reading about this but don't really see the connection. Maybe someone could kindly help out please?

Thanks