# When can we interchange the derivative with an expectation?

Let $(X_t)$ be a stochastic process, and define a new stochastic process by $Y_t = \int_0^t f(X_s) ds$. Is it true in general that $\frac{d} {dt} \mathbb{E}(Y_t) = \mathbb{E}(f(X_t))$? If not, under what conditions would we be allowed to interchange the derivative operator with the expectation operator?

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@ Jonas : no it is not always true, but if you can interchange expectation and integral term then it is true so you only have to derive the conditions under which such operation is ok. Regards. –  TheBridge Oct 22 '12 at 20:58
Where could I find information about when such an operation is ok? –  jmbejara Dec 4 at 20:04