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Need help for Ito Isometry proof

  1. Aug 16, 2011 #1

    There is one step in Ito Isometry proof I don't understand.

    Bt(w) represents the position of w at time t, then E[(Btj+1(w)-Btj(w))2] = tj+1 - tj.

    Why is the expectation of the square of the difference of 2 positions equal to their time difference?

    Any hint, please.

    Thank you.
  2. jcsd
  3. Aug 18, 2011 #2
    Could you clarify what Bt(w) is & whether it's normally distributed?
  4. Aug 18, 2011 #3
    I'm guessing B_t(w) is Brownian motion, and yes it's normally distributed because its increments, B_t(w) - B_s(w) are normally distributed (~ N(0, t-s)) if s < t. Indeed, this is the precise property that gives the result the OP wants to understand.
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