{"title":"Infinite-dimensional calculus under weak spatial regularity of the processes","issue":"2","quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s10959-016-0724-2","publication":"Journal of Theoretical Probability","_id":"1215","pubrep_id":"712","language":[{"iso":"eng"}],"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"oa":1,"date_published":"2018-06-01T00:00:00Z","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"abstract":[{"lang":"eng","text":"Two generalizations of Itô formula to infinite-dimensional spaces are given.\r\nThe first one, in Hilbert spaces, extends the classical one by taking advantage of\r\ncancellations when they occur in examples and it is applied to the case of a group\r\ngenerator. The second one, based on the previous one and a limit procedure, is an Itô\r\nformula in a special class of Banach spaces having a product structure with the noise\r\nin a Hilbert component; again the key point is the extension due to a cancellation. This\r\nextension to Banach spaces and in particular the specific cancellation are motivated\r\nby path-dependent Itô calculus."}],"page":"789-826","publication_status":"published","month":"06","date_updated":"2021-01-12T06:49:09Z","ddc":["519"],"file":[{"checksum":"47686d58ec21c164540f1a980ff2163f","relation":"main_file","content_type":"application/pdf","file_size":671125,"access_level":"open_access","date_updated":"2020-07-14T12:44:39Z","file_id":"5266","file_name":"IST-2016-712-v1+1_s10959-016-0724-2.pdf","date_created":"2018-12-12T10:17:13Z","creator":"system"}],"publisher":"Springer","volume":31,"day":"01","oa_version":"Published Version","file_date_updated":"2020-07-14T12:44:39Z","intvolume":"        31","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The second named author benefited partially from the support of the “FMJH Program Gaspard Monge in Optimization and Operations Research” (Project 2014-1607H). He is also grateful for the invitation to the Department of Mathematics of the University of Pisa. The third named author is grateful for the invitation to ENSTA.","scopus_import":1,"publist_id":"6119","date_created":"2018-12-11T11:50:45Z","year":"2018","citation":{"ieee":"F. Flandoli, F. Russo, and G. A. Zanco, “Infinite-dimensional calculus under weak spatial regularity of the processes,” <i>Journal of Theoretical Probability</i>, vol. 31, no. 2. Springer, pp. 789–826, 2018.","ama":"Flandoli F, Russo F, Zanco GA. Infinite-dimensional calculus under weak spatial regularity of the processes. <i>Journal of Theoretical Probability</i>. 2018;31(2):789-826. doi:<a href=\"https://doi.org/10.1007/s10959-016-0724-2\">10.1007/s10959-016-0724-2</a>","mla":"Flandoli, Franco, et al. “Infinite-Dimensional Calculus under Weak Spatial Regularity of the Processes.” <i>Journal of Theoretical Probability</i>, vol. 31, no. 2, Springer, 2018, pp. 789–826, doi:<a href=\"https://doi.org/10.1007/s10959-016-0724-2\">10.1007/s10959-016-0724-2</a>.","chicago":"Flandoli, Franco, Francesco Russo, and Giovanni A Zanco. “Infinite-Dimensional Calculus under Weak Spatial Regularity of the Processes.” <i>Journal of Theoretical Probability</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s10959-016-0724-2\">https://doi.org/10.1007/s10959-016-0724-2</a>.","ista":"Flandoli F, Russo F, Zanco GA. 2018. Infinite-dimensional calculus under weak spatial regularity of the processes. Journal of Theoretical Probability. 31(2), 789–826.","short":"F. Flandoli, F. Russo, G.A. Zanco, Journal of Theoretical Probability 31 (2018) 789–826.","apa":"Flandoli, F., Russo, F., &#38; Zanco, G. A. (2018). Infinite-dimensional calculus under weak spatial regularity of the processes. <i>Journal of Theoretical Probability</i>. Springer. <a href=\"https://doi.org/10.1007/s10959-016-0724-2\">https://doi.org/10.1007/s10959-016-0724-2</a>"},"type":"journal_article","author":[{"full_name":"Flandoli, Franco","last_name":"Flandoli","first_name":"Franco"},{"first_name":"Francesco","full_name":"Russo, Francesco","last_name":"Russo"},{"first_name":"Giovanni A","last_name":"Zanco","id":"47491882-F248-11E8-B48F-1D18A9856A87","full_name":"Zanco, Giovanni A"}],"status":"public","department":[{"_id":"JaMa"}],"has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)"}