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Prove $\int_{0}^{t} W_s dW_s=1/2 {W_t}^2-1/2t$ using Ito's formulas.

I don't really know how to approach this problem since I'm not given a function to find it's derivatives and plug into the Ito's formula which is:

$Y_t=f(0,0)+\int_{0}^{t}[\frac{df}{dx}(s,W_s)]dW_s+\int_{0}^{t}[\frac{df}{dt}(s,W_s)+\frac{1d^2f}{2dx^2}(s,W_s)]ds$

If I was given some function what I would do is:

  1. Find partial derivatives required,
  2. Plugin into the formula
  3. Play about with it until I get the required
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1 Answer 1

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Here, Page $45$, example 4.1.3.

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  • $\begingroup$ So you do have to pick a function in order to compute this... $\endgroup$
    – GRS
    Nov 25, 2015 at 22:21
  • $\begingroup$ Well.. yes, you do have to do something. $\endgroup$ Nov 26, 2015 at 8:55

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