A Malliavin-Skorohod calculus in L^0 and L^1 for additive and Volterra-type processes
Peer reviewed, Journal article
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Original versionStochastics: An International Journal of Probability and Stochastic Processes. 2017, 89 (1), 142-170. 10.1080/17442508.2016.1140767
In this paper we develop a Malliavin–Skorohod type calculus for additive processes in the L1 and L1 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 L1. 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 alfa-stable processes with alfa < 2. The presentation focuses on jump type processes.