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Re: Reexpressing Var[U^2]
Posted:
Jun 23, 2006 5:15 AM


Konrad Viltersten wrote: > From a formula i have concluded that > Var[U^2] + (ts)^2 = C * (ts)^2, > where U = (W_t  W_s), {W_t} is a Wiener process. > > Obviously, Var[U^2] will be a multiple of (ts)^2. > However, the rephrasing below is not generally valid. > Var[U^2] = Var[U]^2 > How can i motivate that transition. >
If U is zeromean normal random variable, then Var[U^2]=E[(U^2)^2]=E[U^4], i.e. the fourth moment of U. The formulae for the higher moments of normal rvs you know?
Ciao
karl



