{"publication":"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.","publication_status":"published","issue":"2","doi":"10.1016/j.jmaa.2009.08.041","page":"383 - 398","type":"journal_article","_id":"2124","oa":1,"volume":363,"abstract":[{"text":"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.","lang":"eng"}],"publist_id":"4912","date_updated":"2021-01-12T06:55:27Z","author":[{"full_name":"Jan Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","orcid":"0000-0002-0845-1338","last_name":"Maas"}],"status":"public","date_created":"2018-12-11T11:55:51Z","publisher":"Academic Press","day":"15","year":"2010","month":"03","extern":1,"date_published":"2010-03-15T00:00:00Z","citation":{"ieee":"J. Maas, “Malliavin calculus and decoupling inequalities in Banach spaces,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 363, no. 2. Academic Press, pp. 383–398, 2010.","ama":"Maas J. Malliavin calculus and decoupling inequalities in Banach spaces. <i>Journal of Mathematical Analysis and Applications</i>. 2010;363(2):383-398. doi:<a href=\"https://doi.org/10.1016/j.jmaa.2009.08.041\">10.1016/j.jmaa.2009.08.041</a>","short":"J. Maas, Journal of Mathematical Analysis and Applications 363 (2010) 383–398.","mla":"Maas, Jan. “Malliavin Calculus and Decoupling Inequalities in Banach Spaces.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 363, no. 2, Academic Press, 2010, pp. 383–98, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2009.08.041\">10.1016/j.jmaa.2009.08.041</a>.","apa":"Maas, J. (2010). Malliavin calculus and decoupling inequalities in Banach spaces. <i>Journal of Mathematical Analysis and Applications</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jmaa.2009.08.041\">https://doi.org/10.1016/j.jmaa.2009.08.041</a>","ista":"Maas J. 2010. Malliavin calculus and decoupling inequalities in Banach spaces. Journal of Mathematical Analysis and Applications. 363(2), 383–398.","chicago":"Maas, Jan. “Malliavin Calculus and Decoupling Inequalities in Banach Spaces.” <i>Journal of Mathematical Analysis and Applications</i>. Academic Press, 2010. <a href=\"https://doi.org/10.1016/j.jmaa.2009.08.041\">https://doi.org/10.1016/j.jmaa.2009.08.041</a>."},"intvolume":"       363","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0801.2899"}],"quality_controlled":0,"title":"Malliavin calculus and decoupling inequalities in Banach spaces"}