Asymptotic Expansion and Weak Approximation: Applications of Malliavin Calculus and Deep Learning (SpringerBriefs in Statistics) - Softcover

Takahashi, Akihiko; Yamada, Toshihiro

Softcover

ISBN 10: 9819682797 ISBN 13: 9789819682799

Publisher: Springer, 2025

Synopsis

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.

About this title

About the Author

Akihiko Takahashi is at Graduate School of Economics, The University of Tokyo

Toshihiro Yamada is at Graduate School of Economics, Hitotsubashi University

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2025
• Language: English
• ISBN 10: 9819682797
• ISBN 13: 9789819682799
• Binding: Paperback
• Number of pages: 109