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Sum of Brownian Motions

  1. Apr 12, 2013 #1
    B(t) is a standard Brownian Motion. u and v are both => 0. What is the distribution of B(u) + B(v)?

    The mean is 0.

    For the variance I get Var(B(u)+B(v)) = u+v. Is this right?
     
  2. jcsd
  3. Apr 12, 2013 #2

    Ray Vickson

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    How did you get this?
     
  4. Apr 13, 2013 #3
    Aren't B(u) and B(v) independent? If so, then the variance of their sum should be the sum of their variance.
     
  5. Apr 13, 2013 #4

    Ray Vickson

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    Is ##\text{Var}( B(1) + B(1))## equal to 2? Is ##2^2## equal to 2?
     
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