The generalized covariation process and Ito formula

Francesco Russo and Pierre Vallois

Stochastic Processes and their Applications, 1995, vol. 59, issue 1, 81-104

Abstract: 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. We calculate covariation for some important examples arising from anticipating stochastic calculus and we establish a Itô formula for f(X), where f is of class and X admits a generalized bracket [x, X].

Date: 1995
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