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Topic: Re-expressing Var[U^2]
Replies: 1   Last Post: Jun 23, 2006 5:15 AM

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Karl Breitung

Posts: 128
Registered: 12/13/04
Re: Re-expressing Var[U^2]
Posted: Jun 23, 2006 5:15 AM
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Konrad Viltersten wrote:
> From a formula i have concluded that
> Var[U^2] + (t-s)^2 = C * (t-s)^2,
> where U = (W_t - W_s), {W_t} is a Wiener process.
>
> Obviously, Var[U^2] will be a multiple of (t-s)^2.
> However, the rephrasing below is not generally valid.
> Var[U^2] = Var[U]^2
> How can i motivate that transition.
>


If U is zero-mean 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



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