Derivative of Stochastic Function

[Apteronotus]

Hi,

A quick question regarding random functions.
Suppose $$\xi(t)$$ is a stochastic function. In other words, its value at time t is random with some known distribution (Gaussian, say).
Is there any way of calculating $$\frac{d\xi}{dt}$$?

Thanks,

 

[Bob_for_short]

No, there is not. A derivative should not depend on the way of tending the difference df to zero if dt is small. In case of a stochastic (=discontinuous) function it is not the case.

 

[Apteronotus]

So how can we calculate $$\frac{d\xi}{dt}$$?

 

[Bob_for_short]

There is no a preferable way to calculate df/dt in your case.