Stochastic Calculus with Respect to Gaussian Processes

Abstract

In this paper we develop a stochastic calculus with respect to a Gaussian process of the form Bt=∫t0K(t,s)dWs, where W is a Wiener process and K(t,s) is a square integrable kernel, using the techniques of the stochastic calculus of variations. We deduce change-of-variable formulas for the indefinite integrals and we study the approximation by Riemann sums.The particular case of the fractional Brownian motion is discussed.