Ito Calculus

Let $W_t$ be the Wiener process. Let $X_t$ be the Ito process, i.e. $dX_t = \mu dt + \sigma dW_t$ for some functions $\mu$ and $\sigma$ of $X_t$ and $t$.

Then, for twice differentiable function $f$ on $X_t$, $$df(X_t) = f'(X_t) dX_t + \frac{1}{2} \sigma^2 f(X_t) dt,$$ and $f(X_t)$ is also an Ito process.