{"product_id":"9789819682799","title":"SpringerBriefs in Statistics: Applications of Malliavin Calculus and Deep Learning","description":"\u003ch1\u003eSpringerBriefs in Statistics: Applications of Malliavin Calculus and Deep Learning\u003c\/h1\u003e \u003ch2\u003eTakahashi, Akihiko; Yamada, Toshihiro\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp class=\"MsoNormal\"\u003e\u003cspan style=\"mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;\"\u003eThis book provides a self-contained lecture on a Malliavin calculus approach to asymptotic expansion and weak approximation of stochastic differential equations (SDEs),  along with numerical methods for computing parabolic partial differential equations (PDEs). \u003cbr\u003eConstructions of weak approximation and asymptotic expansion are given in detail using Malliavin’s integration by parts with theoretical convergence analysis. \u003cbr\u003eWeak approximation algorithms and Python codes are available with numerical examples. \u003cbr\u003eMoreover, the weak approximation scheme is effectively applied to high-dimensional nonlinear problems without suffering from the curse of dimensionality \u003cbr\u003ethrough combining with a deep learning method. \u003cbr\u003eReaders including graduate-level students, researchers, and practitioners can understand both theoretical and applied aspects of recent developments of asymptotic expansion and weak approximation.\u003c\/span\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2025-10-03\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9789819682799\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-981-96-8280-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 97\u003c\/p\u003e ","brand":"Springer Nature Singapore","offers":[{"title":"Default Title","offer_id":44309299757196,"sku":"9789819682799","price":44.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789819682799.jpg?v=1775048433","url":"https:\/\/lateknightbooks.com\/products\/9789819682799","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}