Noise-Induced Phenomena in Slow-fast Dynamical Systems

A Sample-Paths Approach

Nils Berglund, Barbara Gentz - Collection Probability and Its Applications

278 pages, parution le 25/01/2006

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Résumé

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. The emphasis lies on noise-induced phenomena such as stochastic resonance, hysteresis, excitability, and the reduction of bifurcation delay.

Sommaire

Introduction
Deterministic Slow-Fast Systems
One-Dimensional Slowly Time-Dependent Systems
Stochastic Resonance
Multi-Dimensional Slow-Fast Systems
Applications
A: A Brief Introduction to Stochastic Differential Equations
B: Some Useful Inequalities
C: First-Passage Times for Gaussian Processes
References
List of Symbols and Acronyms
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Nils Berglund, Barbara Gentz
Collection	Probability and Its Applications
Parution	25/01/2006
Nb. de pages	278
Format	16 x 24
Couverture	Relié
Poids	534g
Intérieur	Noir et Blanc
EAN13	9781846280382
ISBN13	978-1-84628-038-2