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A Malliavin-Skorohod calculus in L^0 and L^1 for additive and Volterra-type processes

Di Nunno, Giulia; Vives, Josep
Peer reviewed, Journal article
Accepted version
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URI
http://hdl.handle.net/11250/2490296
Date
2017
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  • Publikasjoner fra CRIStin (NHH) [243]
Original version
Stochastics: An International Journal of Probability and Stochastic Processes. 2017, 89 (1), 142-170.   10.1080/17442508.2016.1140767
Abstract
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.
Journal
Stochastics: An International Journal of Probability and Stochastic Processes

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