Asymptotic Expansion and Weak Approximation
Applications of Malliavin Calculus and Deep Learning
Series: SpringerBriefs in Statistics;
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Product details:
- Publisher Springer Nature Singapore
- Date of Publication 9 October 2025
- Number of Volumes 1 pieces, Book
- ISBN 9789819682799
- Binding Paperback
- No. of pages96 pages
- Size 235x155 mm
- Language English
- Illustrations XII, 96 p. 4 illus., 3 illus. in color. Illustrations, black & white 700
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Long description:
"
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.
Table of Contents:
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.
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