# On the second derivative of Wiener process

As we all know, continuous white noise is the derivative, with respect to time, of a Wiener process.

My question is that does the second derivative of Wiener process exists? If so, what is it and how about its first and second moment characteristics? Thanks.

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Hi, Nate, you rise a good question. The first derivative exits in mean sense. So in the classical sense, it may fail to find it. –  eolithr Jul 13 at 14:56
I agree with @NateEldredge that this question does not seem to be research level, and surely can be answered on MSE, so I flagged it. –  Ilya Jul 17 at 13:32
Regardless of whether the question will be migrated or not, please give the precise meaning of "The first derivative exists in mean sense". It is also the way you would like to find the second derivative - "in mean sense"? –  Ilya Jul 17 at 13:34
(The OP's first comment refers to Nate Eldredge's comment "You have to say in what sense you want to consider these derivatives. In the classical sense, even the first derivative doesn't exist." which got auto-deleted in the migration.) –  Willie Wong Jul 17 at 15:27