{"product_id":"asymptotic-expansion-and-weak-approximation-akihiko-takahashi-9789819682799","title":"Asymptotic Expansion and Weak Approximation: Applications of Malliavin Calculus and Deep Learning","description":"This 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Akihiko Takahashi,Toshihiro Yamada\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9819682797\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789819682799\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/03\/2025\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 97\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.37lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.23d","brand":"Akihiko Takahashi","offers":[{"title":"Paperback","offer_id":47425715306751,"sku":"9789819682799","price":49.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_c91870c7-df2b-4023-8cde-051f14690f1b.jpg?v=1761541128","url":"https:\/\/www.whiterainbookhouse.com\/products\/asymptotic-expansion-and-weak-approximation-akihiko-takahashi-9789819682799","provider":"WR Book House","version":"1.0","type":"link"}