Geometry and Invariance in Stochastic Dynamics: Verona, Italy, March 25-29, 2019

This book explores the invariance and symmetry properties of finite and infinite dimensional stochastic differential equations, extending the theory of classical differential equations. It aims to bridge the gap between deterministic and stochastic approaches and contribute to the development of a unified theory with applications in stochastic modelling.

Format: Paperback / softback
Length: 265 pages
Publication date: 10 February 2023
Publisher: Springer Nature Switzerland AG

This book is a comprehensive exploration of the field of invariance and symmetry properties of finite and infinite dimensional stochastic differential equations. It emerged from the Random Transformations and Invariance in Stochastic Dynamics conference, held in Verona from March 25th to 28th, 2019, in honor of Sergio Albeverio. This area represents a significant and necessary extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance has proven invaluable for both theoretical and numerical studies, leading to numerous important applications.

The primary objective of this book is to provide a comprehensive overview of the current state of research in stochastic systems from this perspective. It will introduce fundamental concepts and methodologies involved, while also outlining the major directions for future advancements. The central focus lies in bridging the gap between deterministic and stochastic approaches, aiming to contribute to the development of a unified theory that will have a profound impact on both theoretical and applied domains.

The intended audience for this book includes mathematicians and theoretical physicists with a strong background in stochastic analysis, drawing inspiration from mathematical physics and Lie group geometry. While primarily aimed at academicians, this text can also be valuable to practitioners with a Ph.D. who are interested in efficient stochastic modeling.

In summary, this book offers a comprehensive and up-to-date introduction to the field of invariance and symmetry properties of stochastic differential equations, providing a valuable resource for scholars and practitioners alike. Its interdisciplinary nature and application-oriented approach make it an essential read for anyone seeking to advance their understanding of these complex mathematical systems.

Weight: 433g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030874346
Edition number: 1st ed. 2021