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Math Help - Standard Deviation of a Wiener Process

  1. #1
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    Standard Deviation of a Wiener Process

    Before I state my question, I'll quote my textbook on financial derivatives:

    [...] A generalized Wiener process for a variable x can be defined in terms of dz as

    dx = a dt + b dz (12.3)

    [...] The b dz term on the right-hand side of equation (12.3) can be regarded as adding noise or variability to the path followed by x. The amount of this noise or variability is b times a Wiener process. A Wiener process has standard deviation of 1.0. It follows that b times a Wiener process has a standard deviation of b.
    I'm not very good at math, so this is why I'm asking this question. I thought it wasn't possible to multiply st. dev., only variance. Then why is the st. dev. of a generalized Wiener process b times 1.0? Thanks
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  2. #2
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    The Wiener process rings a bell here ))) which text book are you using?

    To answer your question, I'd say if std variation is 1, the variance is also 1, so it gives b in either case.
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