Authors:
- The approach used here allows researchers and practitioners to quantitatively describe domains in a way that is close to reality - this is the first approach to do this
- Several concrete examples are described in detail to show how the method works in practice. The examples are from physics and climatology - two of the main disciplines to use these methods
- Includes supplementary material: sn.pub/extras
Part of the book series: Probability and Its Applications (PIA)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is aimed at advanced undergraduate and graduate students, and researchers in mathematics, physics, the natural sciences, and engineering. It presents a new constructive approach to the quantitative description of solutions to systems of stochastic differential equations evolving on well-separated timescales. The method, which combines techniques from stochastic analysis and singular perturbation theory, allows the domains of concentration for typical sample paths to be determined, and provides precise estimates on the transition probabilities between these domains.
In addition to the detailed presentation of the set-up and mathematical results, applications to problems in physics, biology, and climatology are discussed.
Reviews
From the reviews:
"This well-written book presents an approach based on a series of articles of both authors. The main aim is a characterisation of typical sample paths for slow-fast systems. Presenting a detailed exposition of the setup and mathematical results, as well as a path to recent applied research, the book is aimed at a wide range of readers, from advanced students to researchers in mathematics, physics, or engineering." (Dirk Blömker, Mathematical Reviews, Issue 2007 b)
Authors and Affiliations
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Centre de Physique Theorique, Marseille Cedex 9, France
Nils Berglund
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Weierstrasse Institute for Applied, Analysis and Stochastics, Berlin, Germany
Barbara Gentz
Bibliographic Information
Book Title: Noise-Induced Phenomena in Slow-Fast Dynamical Systems
Book Subtitle: A Sample-Paths Approach
Authors: Nils Berglund, Barbara Gentz
Series Title: Probability and Its Applications
DOI: https://doi.org/10.1007/1-84628-186-5
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2006
Hardcover ISBN: 978-1-84628-038-2Published: 19 December 2005
Softcover ISBN: 978-1-84996-547-7Published: 21 October 2010
eBook ISBN: 978-1-84628-186-0Published: 07 February 2006
Series ISSN: 1431-7028
Edition Number: 1
Number of Pages: XIII, 276
Number of Illustrations: 57 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Dynamical Systems and Ergodic Theory, Statistics, general, Numerical and Computational Physics, Simulation