Asymptotic Expansion and Weak Approximation

Applications of Malliavin Calculus and Deep Learning
Erscheinungsjahr 2025
ISBN: 978-981-968279-9
Verlag: Springer

Buch, Englisch, 97 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 184 g

Reihe: JSS Research Series in Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Takahashi, Akihiko

Yamada, Toshihiro

Fachgebiete

• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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.

Über Autor(innen)

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

Toshihiro Yamada is at Graduate School of Economics, Hitotsubashi University