{"status":"public","day":"15","date_updated":"2021-01-12T06:55:27Z","_id":"2124","year":"2010","extern":1,"volume":363,"quality_controlled":0,"publication_status":"published","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0801.2899"}],"intvolume":"       363","publist_id":"4912","issue":"2","doi":"10.1016/j.jmaa.2009.08.041","publication":"Journal of Mathematical Analysis and Applications","type":"journal_article","title":"Malliavin calculus and decoupling inequalities in Banach spaces","date_published":"2010-03-15T00:00:00Z","page":"383 - 398","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.","date_created":"2018-12-11T11:55:51Z","publisher":"Academic Press","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"}],"author":[{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","full_name":"Jan Maas"}],"month":"03","oa":1,"citation":{"short":"J. Maas, Journal of Mathematical Analysis and Applications 363 (2010) 383–398.","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>","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>.","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.","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."}}