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Asymptotic Expansion and Weak Approximation: Applications of Malliavin Calculus and Deep Learning - Couverture souple

Takahashi, Akihiko; Yamada, Toshihiro

 
9789819682799: Asymptotic Expansion and Weak Approximation: Applications of Malliavin Calculus and Deep Learning
Couverture souple
ISBN 10 : 9819682797 ISBN 13 : 9789819682799
Editeur : 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

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

Toshihiro Yamada is at Graduate School of Economics, Hitotsubashi University

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
2025
Langue
anglais
ISBN 10 
9819682797
ISBN 13 
9789819682799
Reliure
Broché
Nombre de pages
112
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