SDE: conditions for the process to be normal and/or stationary

Question

We have random process $X(t)$ satisfying the following SDE: $dX(t)=A(X(t))dt+B(X(t))dW(t)$, with $W(t)$ - Wiener process.

Does somebody know sufficient/necessary conditions on $A$ and $B$, that the random process $X(t)$ is normal and/or stationary?

I would be grateful for the literature, also in the complex case.

Answer 1

I recommend the following book on:

Stochastic Stability of Differential Equations

Specifically Chapter 3 if I recall correctly.