Asymptotic Expansion and Weak Approximation
Applications of Malliavin Calculus and Deep Learning
Seiten
2025
Springer Nature Switzerland AG (Verlag)
978-981-96-8279-9 (ISBN)
Springer Nature Switzerland AG (Verlag)
978-981-96-8279-9 (ISBN)
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mso-bidi-language: AR-SA;">This book provides a self-contained lecture on a Malliavin calculus approach to asymptotic expansion and weak approximation of stochastic differential equations (SDEs) as well as numerical methods for computing parabolic partial differential equations (PDEs).
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.
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.
Akihiko Takahashi is at Graduate School of Economics, The University of Tokyo Toshihiro Yamada is at Graduate School of Economics, Hitotsubashi University
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.
| Erscheinungsdatum | 13.06.2025 |
|---|---|
| Reihe/Serie | JSS Research Series in Statistics | SpringerBriefs in Statistics |
| Zusatzinfo | 3 Illustrations, color; 1 Illustrations, black and white |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | asymptotic expansion • Deep learning • Malliavin calculus • SDE • stochastic differential equation • Weak Approximation |
| ISBN-10 | 981-96-8279-7 / 9819682797 |
| ISBN-13 | 978-981-96-8279-9 / 9789819682799 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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