Malliavin calculus and decoupling inequalities in Banach spaces

Maas J. 2010. Malliavin calculus and decoupling inequalities in Banach spaces. Journal of Mathematical Analysis and Applications. 363(2), 383–398.


Journal Article | Published
Abstract
We develop a theory of Malliavin calculus for Banach space-valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Itô isometry to Banach spaces. In the white noise case we obtain two sided Lp-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-Itô chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the opposite direction we use Meyer's inequalities to give a new proof of a decoupling result for Gaussian chaoses in UMD Banach spaces.
Publishing Year
Date Published
2010-03-15
Journal Title
Journal of Mathematical Analysis and Applications
Acknowledgement
The author acknowledges support by the ‘VIDI subsidie’ 639.032.201 of the Netherlands Organisation for Scientific Research (NWO) and the ARC Discovery Grant DP0558539.
Volume
363
Issue
2
Page
383 - 398
IST-REx-ID

Cite this

Maas J. Malliavin calculus and decoupling inequalities in Banach spaces. Journal of Mathematical Analysis and Applications. 2010;363(2):383-398. doi:10.1016/j.jmaa.2009.08.041
Maas, J. (2010). Malliavin calculus and decoupling inequalities in Banach spaces. Journal of Mathematical Analysis and Applications. Academic Press. https://doi.org/10.1016/j.jmaa.2009.08.041
Maas, Jan. “Malliavin Calculus and Decoupling Inequalities in Banach Spaces.” Journal of Mathematical Analysis and Applications. Academic Press, 2010. https://doi.org/10.1016/j.jmaa.2009.08.041.
J. Maas, “Malliavin calculus and decoupling inequalities in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 363, no. 2. Academic Press, pp. 383–398, 2010.
Maas J. 2010. Malliavin calculus and decoupling inequalities in Banach spaces. Journal of Mathematical Analysis and Applications. 363(2), 383–398.
Maas, Jan. “Malliavin Calculus and Decoupling Inequalities in Banach Spaces.” Journal of Mathematical Analysis and Applications, vol. 363, no. 2, Academic Press, 2010, pp. 383–98, doi:10.1016/j.jmaa.2009.08.041.
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