We construct and study a wide class of stationary increment Gaussian processes and their associated stochastic calculus. The underlying framework is set within the White Noise space, a setting which allows to study a wide range of processes, among them, processes being not necessarily semi-martingales (e.g., the fractional Brownian motion), as well as their derivatives, understood as stochastic distributions. The Wick product is defined. A subsequent construction of an associated Wick-Ito stochastic integrals as a limit of Riemann sums, is then shown to generalize the well known Ito and Skorohod stochastic integrals. The derivation of an Ito formula follows.
The talk is based on joint works with Daniel Alpay, Haim Attia and Palle Jorgensen.
Bienvenue à tous!