LEADER 03193nam 22006495 450 001 9911031564503321 005 20260225161127.0 010 $a981-9682-80-0 024 7 $a10.1007/978-981-96-8280-5 035 $a(MiAaPQ)EBC32327622 035 $a(Au-PeEL)EBL32327622 035 $a(CKB)41537096500041 035 $a(DE-He213)978-981-96-8280-5 035 $a(OCoLC)1549519898 035 $a(EXLCZ)9941537096500041 100 $a20251002d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAsymptotic Expansion and Weak Approximation $eApplications of Malliavin Calculus and Deep Learning /$fby Akihiko Takahashi, Toshihiro Yamada 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (177 pages) 225 1 $aJSS Research Series in Statistics,$x2364-0065 311 08$a981-9682-79-7 327 $aChapter 1. Introduction -- Chapter 2. Itô calculus -- Chapter 3. Malliavin calculus -- Chapter 4. Asymptotic expansion -- Chapter 5. Weak approximation -- Chapter 6. Application: Deep learning-based weak approximation. 330 $aThis book provides a self-contained lecture on a Malliavin calculus approach to asymptotic expansion and weak approximation of stochastic differential equations (SDEs), along with numerical methods for computing parabolic partial differential equations (PDEs). Constructions of weak approximation and asymptotic expansion are given in detail using Malliavin?s integration by parts with theoretical convergence analysis. Weak approximation algorithms and Python codes are available with numerical examples. Moreover, the weak approximation scheme is effectively applied to high-dimensional nonlinear problems without suffering from the curse of dimensionality through combining with a deep learning method. Readers including graduate-level students, researchers, and practitioners can understand both theoretical and applied aspects of recent developments of asymptotic expansion and weak approximation. 410 0$aJSS Research Series in Statistics,$x2364-0065 606 $aStatistics 606 $aMathematical statistics$xData processing 606 $aStatistics 606 $aStatistical Theory and Methods 606 $aStatistics and Computing 606 $aApplied Statistics 606 $aProbabilitats$2thub 606 $aProcessos estocāstics$2thub 608 $aLlibres electrōnics$2thub 615 0$aStatistics. 615 0$aMathematical statistics$xData processing. 615 0$aStatistics. 615 14$aStatistical Theory and Methods. 615 24$aStatistics and Computing. 615 24$aApplied Statistics. 615 7$aProbabilitats 615 7$aProcessos estocāstics 676 $a519.5 700 $aTakahashi$b Akihiko$01850751 701 $aYamada$b Toshihiro$01850752 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911031564503321 996 $aAsymptotic Expansion and Weak Approximation$94443936 997 $aUNINA