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Asymptotic expansion and weak approximationapplications of Malliavin calculus and deep learning /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Asymptotic expansion and weak approximationby 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.
Contained By:	Springer Nature eBook
Subject:	Stochastic differential equations.
Online resource:	https://doi.org/10.1007/978-981-96-8280-5
ISBN:	9789819682805$q(electronic bk.)

Asymptotic expansion and weak approximationapplications 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$q(electronic bk.)

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

185784
Stochastic differential equations.

LC Class. No.: QA274.23

Dewey Class. No.: 519.22

Asymptotic expansion and weak approximationapplications of Malliavin calculus and deep learning /
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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.
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