Suppose I have a stochastic process $X_t$ that satisfies the SDE:
where $W_t$ is a Brownian motion. Suppose I haven't made any assumption yet about the functions $\sigma(\cdot)$ and $\mu(\cdot)$ (therefore I don't even know if my SDE has a strong solution, or even a weak one).
Can I use Ito's formula anyway? In other words, is it true that the process $Y_t=f(X_t)$, where $f(\cdot)$ is twice differentiable, follows an SDE
I couldn't find a simple answer in the usual references, any help is welcome.