An Itô-Stratonovich formula for Gaussian processes: A Riemann sums approach (Q952826)

This work is devoted to prove a change-of-variable formula for general Gaussian processes under some technical conditions on the corresponding covariance function. The stochastic integral is defined in the Stratonovich sense using an approximation by middle point Riemann sums. Then the Itô-Stratonovich formula is deduced by means of a Taylor expansion up to the sixth order, where the Malliavin calculus techniques are used to show the convergence to zero of the residual terms. The conditions on the covariance function are weak enough to include processes with infinite quadratic variation. Moreover, the authors prove that they are satisfied by the bifractional Brownian motion with parameters \((H,K)\) such that \(1/6<HK<1\), and, in particular, for the fractional Brownian motion with Hurst parameter \(1/6<H<1\).