A Malliavin–Skorohod calculus in L0 and L1 for additive and Volterra-type processes. Issue 1 (2nd January 2017) - Nunno, Giulia Di; Vives, Josep
Abstract : In this paper we develop a Malliavin–Skorohod type calculus for additive processes in the and settings, extending the probabilistic interpretation of the Malliavin–Skorohod operators to this context. We prove calculus rules and obtain a generalization of the Clark–Hausmann–Ocone formula for random variables in . Our theory is then applied to extend the stochastic integration with respect to volatility modulated Lévy-driven Volterra processes recently introduced in the literature. Our work yields to substantially weaker conditions that permit to cover integration with respect to e.g. Volterra processes driven by -stable processes with . The presentation focuses on jump type processes.