The generalized covariation process and Ito formula

If X and Y are two general stochastic processess, we define a covariation process [X, Y] with the help of a limit procedure. When the processes are semimartingales, [X, Y] is their classical bracket. culate covariation for some important examples arising from anticipating stochastic calculus and we establish a Itô formula for f(X), where f is of class C2(R) and X admits a generalized bracket [x, X].