Symplectic Integration of Stochastic Hamiltonian Systems

This book explores stochastic numerical methods for long-term dynamics in Hamiltonian systems, emphasizing symplectic integration and its applications.

This book offers a comprehensive overview of stochastic numerical methods that capture the long-term dynamic behaviors of both finite and infinite-dimensional stochastic Hamiltonian systems. The focus is on various aspects of long-time dynamics, including symplectic structure, invariants, ergodicity, and invariant measures. By emphasizing the systematic construction of these methods, the text highlights the probabilistic advantages of stochastic symplectic techniques, which are designed to maintain the geometric integrity of the stochastic flow within these systems.

In Symplectic Integration of Stochastic Hamiltonian Systems, the author delves into several intriguing research areas, such as numerical analysis, stochastic analysis, ergodic theory, and the study of stochastic ordinary and partial differential equations. Each of these topics represents a significant frontier in contemporary research, making the book relevant to a broad audience of scholars and practitioners. The interplay between theory and application is a recurring theme, providing readers with insights that can be applied to real-world problems.

This text is particularly appealing to researchers and students who wish to deepen their understanding of the intricate dynamics involved in stochastic Hamiltonian systems. By presenting complex concepts in an accessible manner, Symplectic Integration of Stochastic Hamiltonian Systems serves as both a reference and a guide for those engaged in this evolving field.