A Malliavin–Skorohod calculus in L0 and L1 for additive and Volterra-type processes. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Nunno, Giulia Di; Vives, Josep
• Is Part Of: Stochastics. Volume 89:Issue 1(2017)
• Page Start: 142
• Page End: 170
• Publication Date: 2017-01-02
• Subjects: Additive processes -- Lévy processes -- -stable processes -- Volterra processes -- Malliavin–Skorohod calculus; 60H05 -- 60H07; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2016.1140767
• Languages: English
• ISSNs: 1744-2508

Abstract

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.