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Math Help - Brownian motion

  1. #1
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    Brownian motion

    Let {B}(t) be a Brownian motion. Show that the following processes are Brownian motions on [0,T].

    1. {X}(t)=-{B}(t).

    2. {X}(t)={B}(T-t) - {B}(T), where {T}<+\infty.

    3. {X}(t)=c{B}(t/{c}^2), where {T}\leq+\infty.

    4. {X}(t)=t{B}(1/t),t>0, and {X}(0)=0.

    Who ever can answer all of these is legendary. Any help will be greatly appreciated. Thanks.
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  2. #2
    Junior Member
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    All your questions regarding Brownian motions is simply a matter of applying and checking the definition.

    Definition of Brownian motion:
    A continuous random process X(t) is a (standard) Brownian motion if it satisfies

    1. X(0) = 0
    2. Independent increments
    3. Increments are normally distributed with mean zero and variance equal to the time increment.
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