東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Asymptotic expansion and weak approx...

Takahashi, Akihiko.

Linked to FindBook

Google Book

Amazon

博客來

Asymptotic expansion and weak approximation = applications of Malliavin calculus and deep learning /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Asymptotic expansion and weak approximation/ by Akihiko Takahashi, Toshihiro Yamada.
Reminder of title:	applications of Malliavin calculus and deep learning /
Author:	Takahashi, Akihiko.
other author:	Yamada, Toshihiro.
Published:	Singapore :Springer Nature Singapore : : 2025.,
Description:	xii, 97 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Chapter 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.
Contained By:	Springer Nature eBook
Subject:	Stochastic differential equations. -
Online resource:	https://doi.org/10.1007/978-981-96-8280-5
ISBN:	9789819682805

Asymptotic expansion and weak approximation = applications of Malliavin calculus and deep learning /
Takahashi, Akihiko.

Asymptotic expansion and weak approximationapplications of Malliavin calculus and deep learning /[electronic resource] :by Akihiko Takahashi, Toshihiro Yamada. - Singapore :Springer Nature Singapore :2025. - xii, 97 p. :ill. (some col.), digital ;24 cm. - JSS research series in statistics,2364-0065. - JSS research series in statistics..

Chapter 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.

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). 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.

ISBN: 9789819682805

Standard No.: 10.1007/978-981-96-8280-5doiSubjects--Topical Terms:

621860
Stochastic differential equations.

LC Class. No.: QA274.23

Dewey Class. No.: 519.22

Asymptotic expansion and weak approximation = applications of Malliavin calculus and deep learning /
LDR:02240nmm a2200337 a 4500 001 2421801
003 DE-He213
005 20251002130418.0
006 m d
007 cr nn 008maaau
008 260505s2025 si s 0 eng d
020 $a 9789819682805 $q (electronic bk.)
020 $a 9789819682799 $q (paper)
024 7 $a 10.1007/978-981-96-8280-5 $2 doi
035 $a 978-981-96-8280-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274.23
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
082 0 4 $a 519.22 $2 23
090 $a QA274.23 $b .T136 2025
100 1 $a Takahashi, Akihiko. $3 1264632
245 1 0 $a Asymptotic expansion and weak approximation $h [electronic resource] : $b applications of Malliavin calculus and deep learning / $c by Akihiko Takahashi, Toshihiro Yamada.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2025.
300 $a xii, 97 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a JSS research series in statistics, $x 2364-0065
505 0 $a Chapter 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.
520 $a 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). 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.
650 0 $a Stochastic differential equations. $3 621860
650 0 $a Malliavin calculus. $3 648160
650 0 $a Asymptotic expansions. $3 526123
650 0 $a Approximation theory. $3 628068
650 1 4 $a Statistical Theory and Methods. $3 891074
650 2 4 $a Statistics and Computing. $3 3594429
650 2 4 $a Applied Statistics. $3 3300946
700 1 $a Yamada, Toshihiro. $3 3803148
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a JSS research series in statistics. $3 3386949
856 4 0 $u https://doi.org/10.1007/978-981-96-8280-5
950 $a Mathematics and Statistics (SpringerNature-11649)