Asymptotic Expansion and Weak Approximation : Applications of Malliavin Calculus and Deep Learning / by Akihiko Takahashi, Toshihiro Yamada.

Format:

Book

Author/Creator:

Takahashi, Akihiko.

Contributor:

Yamada, Toshihiro.

Series:

JSS Research Series in Statistics, 2364-0065

Language:

English

Subjects (All):

Statistics.

Mathematical statistics--Data processing.

Mathematical statistics.

Statistical Theory and Methods.

Statistics and Computing.

Applied Statistics.

Local Subjects:

Statistical Theory and Methods.

Statistics and Computing.

Applied Statistics.

Physical Description:

1 online resource (177 pages)

Edition:

1st ed. 2025.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2025.

Summary:

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.

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

981-9682-80-0

9789819682805

OCLC:

1549519898