[{"uri_base":"https://research-explorer.ista.ac.at","month":"03","day":"15","dc":{"date":["2010"],"title":["Malliavin calculus and decoupling inequalities in Banach spaces"],"publisher":["Academic Press"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2009.08.041"],"rights":["info:eu-repo/semantics/openAccess"],"source":["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"],"creator":["Jan Maas"],"description":["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."],"identifier":["https://research-explorer.ista.ac.at/record/2124"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"]},"date_published":"2010-03-15T00:00:00Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0801.2899"}],"citation":{"chicago":"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.","short":"J. Maas, Journal of Mathematical Analysis and Applications 363 (2010) 383–398.","mla":"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.","apa":"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","ieee":"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.","ista":"Maas J. 2010. Malliavin calculus and decoupling inequalities in Banach spaces. Journal of Mathematical Analysis and Applications. 363(2), 383–398."},"oa":1,"publication":"Journal of Mathematical Analysis and Applications","page":"383 - 398","quality_controlled":0,"publist_id":"4912","issue":"2","abstract":[{"lang":"eng"}],"extern":1,"type":"journal_article","author":[{"orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","first_name":"Jan"}],"volume":363,"dini_type":"doc-type:article","date_updated":"2021-01-12T06:55:27Z","date_created":"2018-12-11T11:55:51Z","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.","_id":"2124","intvolume":" 363","status":"public","publication_status":"published"}]