{"product_id":"asymptotic-expansion-and-weak-approximation-applications-of-malliavin-calculus-and-deep-learning-paperback","title":"Asymptotic Expansion and Weak Approximation: Applications of Malliavin Calculus and Deep Learning - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eAkihiko Takahashi\u003c\/b\u003e (Author), \u003cb\u003eToshihiro Yamada\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\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\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eAkihiko Takahashi is at Graduate School of Economics, The University of Tokyo\u003c\/p\u003e \u003cp\u003eToshihiro Yamada is at Graduate School of Economics, Hitotsubashi University\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 97\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.23 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 03, 2025\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":48757439594745,"sku":"9789819682799","price":80.98,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/dgnzOTXxJM9789819682799.webp?v=1785946539","url":"https:\/\/bookscloud.io\/products\/asymptotic-expansion-and-weak-approximation-applications-of-malliavin-calculus-and-deep-learning-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}