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Math Help - Brownian motion

  1. #1
    Junior Member elenaas's Avatar
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    Brownian motion

    Could someone help me with this:
    Let be Brownian motion and .Prove that is Brownian motion.
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  2. #2
    MHF Contributor

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    Check that the process A_t=B_{t_0+t}-B_{t_0} satisfies the characteristic properties of Brownian motion: A_0=0, A_t is Gaussian with mean 0 and variance t, A has stationary independent increments, and is almost surely continuous (maybe you know another characterization of B.M. from your lecture; then adapt the sentence). All of these properties are immediate consequences of the same properties for B.
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