O que é Itô process, quadratic covariation?

An Itô process is $X_t = X_0 + \int_0^t\mu_s\,ds + \int_0^t\sigma_s\,dW_s$, written $dX_t = \mu_t\,dt + \sigma_t\,dW_t$, with adapted $\mu$, $\sigma$ such that $\int_0^T|\mu_s|\,ds$ and $\int_0^T\sigma_s^2\,ds$ are finite almost surely. The quadratic covariation of two continuous processes is the limit in probability $[X, Y]_t = \lim\sum_k(X_{t_{k+1}} - X_{t_k})(Y_{t_{k+1}} - Y_{t_k})$; for Itô processes driven by $W^1, W^2$ with $d\langle W^1, W^2\rangle_t = \rho\,dt$, $d[X, Y]_t = \sigma^X_t\sigma^Y_t\rho\,dt$.