Symplectic Integration of Stochastic Hamiltonian Systems

This book provides an accessible overview of stochastic numerical methods for studying long-time dynamical behaviors of stochastic Hamiltonian systems, emphasizing their preservation of geometric structure and probabilistic superiority. It covers various research hotspots in numerical analysis, stochastic analysis, ergodic theory, and rough path theory.

Format: Paperback / softback
Length: 300 pages
Publication date: 22 February 2023
Publisher: Springer Verlag, Singapore

This comprehensive book offers an accessible introduction to stochastic numerical methods, which inherit long-time dynamical behaviors from finite and infinite-dimensional stochastic Hamiltonian systems. The focus of the study lies in examining the intricate long-term dynamics, encompassing symplectic structure, invariants, ergodicity, and invariant measures. The primary emphasis is placed on the systematic development and probabilistic superiority of stochastic symplectic methods, which meticulously preserve the geometric structure of the stochastic flow of stochastic Hamiltonian systems. The problems addressed in this book are closely interconnected with several captivating research hotspots, including numerical analysis, stochastic analysis, ergodic theory, stochastic ordinary and partial differential equations, and rough path theory. This book is of immense interest to researchers who delve into these fields.

Weight: 480g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811976698
Edition number: 1st ed. 2022