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Zbl 1107.60029
Solé, Josep Llu{\'\i}s; Utzet, Frederic; Vives, Josep
Canonical Lévy process and Malliavin calculus.
(English)
[J] Stochastic Processes Appl. 117, No. 2, 165-187 (2007). ISSN 0304-4149

Summary: A suitable canonical Lévy process is constructed in order to study a Malliavin calculus based on a chaotic representation property of Lévy processes proved by {\it K. Itô} [Trans. Am. Math. Soc. 81, 253--263 (1956; Zbl 0073.35303)] using multiple two-parameter integrals. In this setup, the two-parameter derivative $D_{t,x}$ is studied, depending on whether $x=0$ or $x \not= 0$; in the first case, we prove a chain rule; in the second case, a formula by trajectories.
MSC 2000:
*60H07 Stochastic calculus of variations and the Malliavin calculus
60G57 Random measures

Keywords: Skorokhod integral

Citations: Zbl 0073.35303

Cited in: Zbl 1164.60041

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