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Math Help - Prove martingale

  1. #1
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    Prove martingale

    Hi all, I have been asked to prove the following process is martingale:
    exp{aX(t) - 1/2 * a^2t} where X(t) is a standard Brownian motion. I'm stuck with this question and would really appreciate it if anyone could give me any suggestions on how to do it. Thanks very much in advance!
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  2. #2
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    i would start by writing the process as a stochastic differential equation using ito's lemma. if the process is indeed a martingale, the drift term (dt) in ito should fall out. you will be left with your diffusion term. from here, you only need prove that the SDE is integrable.
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