Overview
- Gives an introduction to symplectic structure and stochastic variational principle for stochastic Hamiltonian systems
- Provides symplectic and conformal symplectic methods and ergodic methods via stochastic generating function
- Presents the superiority of symplectic methods for stochastic Hamiltonian systems based on large deviation theory
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2314)
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Table of contents (4 chapters)
Keywords
About this book
This book provides an accessible overview concerning the stochastic numerical methods inheriting long-time dynamical behaviours of finite and infinite-dimensional stochastic Hamiltonian systems. The long-time dynamical behaviours under study involve symplectic structure, invariants, ergodicity and invariant measure. The emphasis is placed on the systematic construction and the probabilistic superiority of stochastic symplectic methods, which preserve the geometric structure of the stochastic flow of stochastic Hamiltonian systems.
The problems considered in this book are related to several fascinating research hotspots: numerical analysis, stochastic analysis, ergodic theory, stochastic ordinary and partial differential equations, and rough path theory. This book will appeal to researchers who are interested in these topics.Authors and Affiliations
About the authors
Jialin Hong is a professor at the Chinese Academy of Sciences. He obtained his Ph.D. in 1994 at Jilin University. He works in various directions including structure-preserving algorithms for dynamical systems involving symplectic and multi-symplectic methods for Hamiltonian ODEs and PDEs, Lie group methods and applications, numerical dynamics including chaos, bifurcations for discrete systems, numerical methods for stochastic ordinary differential systems, stochastic partial differential equations and backward stochastic differential equations, almost periodic dynamical systems, and ergodic theory.
Liying Sun is a postdoctoral researcher in the Chinese Academy of Sciences. She works in stochastic differential equations and their numerical methods. She has been investigating regularity properties and strong convergence of numerical approximations for stochastic partial differential equations, weak convergence and numerical longtime behaviors of numerical approximations for stochastic partial differential equations, structure-preserving numerical methods including symplectic integrators and energy-preserving integrators for stochastic Hamiltonian system.
Bibliographic Information
Book Title: Symplectic Integration of Stochastic Hamiltonian Systems
Authors: Jialin Hong, Liying Sun
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-981-19-7670-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022
Softcover ISBN: 978-981-19-7669-8Published: 22 February 2023
eBook ISBN: 978-981-19-7670-4Published: 21 February 2023
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 300
Number of Illustrations: 1 b/w illustrations
Topics: Numerical Analysis, Dynamical Systems and Ergodic Theory, Probability Theory and Stochastic Processes