Stochastic Calculus with Respect to Gaussian Processes

In this paper we develop a stochastic calculus with respect to a Gaussian process of the form Bₜ = ∫ᵗ₀ K(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.