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Math Help - Exponential of a Brownian motion

  1. #1
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    Exponential of a Brownian motion

    How do I calculate the expectation of the exponential of a Brownian motion in an easy way, I mean this:

     E[Exp(a W_{t})]

    With  W_{t} a Brownian motion

    Thx for the help
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  2. #2
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    Write it out in integral form
    <br />
\int e^{a x} (2\pi t)^{-1/2}e^{-\frac{x^2}{2t}} dx.<br />
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