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When $X$ satisfies $${\rm d}X_t=\varphi_t{\rm d}t+\Phi_t{\rm d}W_t$$ on a Hilbert space $H$, where $W$ is a $Q$-Wiener process on a Hilbert space $U$, we know by the Ito formula that $$\|X_t\|_H^2-\|...

Consider the following $n$-dimensional Ito-SDE: \begin{align} dX_t = \mu(X_t,t)dt + \sigma(X_t,t)dW_t \end{align} What are the necessary regularity conditions on $\mu$ and $\sigma$ to ensure that the ...