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Stochastic differential of a particular martingale

  1. Oct 13, 2011 #1
    Hello everyone,
    I'm studying from Oksendal's book, and I'm stuck at an excercise which asks you to find the differential form of:

    X(t) = (W(t)[itex]^{2}[/itex]-t)[itex]^{2}[/itex] - 4[itex]\int[/itex] (W(s))[itex]^{2}[/itex]ds
    where W(t) is a Brownian Motion.

    I tried several possible functions g(t,W(t)) which could have led to a potential solution (by finding d(g(t,W(t))) with Ito), but none led me any closer to a solution.

    Can you please put me in the right direction?


    PS. I posted this in the wrong place, it should have been in "Homeworks and coursework questions", but I don't know how to move it...
    Last edited: Oct 13, 2011
  2. jcsd
  3. Oct 15, 2011 #2
    Yes Ito's formula only applies to the first term in the sum. For the second term, if the integral is from 0 to t, just apply the stochastic version of the fundamental law of calculus.
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