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Can the differential operator be removed to get the mean/variance of an Ito process?

If $X_t$ is an Ito process, such that: $dX_t = \mu(t, X_t)dt + \sigma(t, Xt)dW_t$ where $W_t$ is a standard brownian motion. Then we can say that: $E(dX_t) = \mu(t, X_t)dt$ and that $Var(dX_t) = \s …
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