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Stochastic Dynamics - Hans Crauel

Stochastic Dynamics

By: Hans Crauel (Editor), Matthias Gundlach (Editor)

Hardcover

Published: 26th March 1999
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This volume gives an account of new and recent developments in the theory of random and, in particular, stochastic dynamical systems. Its purpose is to document and, to some extent, summarise the current state of the field of random dynamical systems beyond the recent monograph, "Random Dynamical Systems" by Ludwig Arnold. The book is intended for an audience of researchers and graduate students from stochastics as well as dynamics. It contains carefully refereed contributions from experts in the field, chosen such that a consistent picture can be given. Recent results on stochastic bifurcation, hyperbolic systems, numerics and asymptotics, more general driving processes for stochastic differential equations, and stochastic analysis on infinite-dimensional manifolds are presented in a comprehensible manner. Several new and exciting insights int o the unexpected variety of dynamical behaviours resulting from the influence of stochastic perturbations are conveyed to the reader.

Preface
Contributors and Speakers
Lectures
Stochastic Dynamics: Building upon Two Cultures
Stability Along Trajectories at a Stochastic Bifurcation Pointp. 1
Bifurcations of One-Dimensional Stochastic Differential Equationsp. 27
P-Bifurcations in the Noisy Duffing-van der Pol Equationp. 49
The Stochastic Brusselator: Parametric Noise Destroys Hopf Bifurcationp. 71
Numerical Approximation of Random Attractorsp. 93
Random Hyperbolic Systemsp. 117
Some Questions in Random Dynamical Systems Involving Real Noise Processesp. 147
Topological, Smooth, and Control Techniques for Perturbed Systemsp. 181
Perturbation Methods for Lyapunov Exponentsp. 209
The Lyapunov Exponent of the Euler Scheme for Stochastic Differential Equationsp. 241
Towards a Theory of Random Numerical Dynamicsp. 259
Canonical Stochastic Differential Equations based on Levy Processes and Their Supportsp. 283
On the Link Between Fractional and Stochastic Calculusp. 305
Asymptotic Curvature for Stochastic Dynamical Systemsp. 327
Stochastic Analysis on (Infinite-Dimensional) Product Manifoldsp. 339
Evolutionary Dynamics in Random Environmentsp. 371
Microscopic and Mezoscopic Models for Mass Distributionsp. 395
Indexp. 432
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387985121
ISBN-10: 0387985123
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 440
Published: 26th March 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.13 x 15.88  x 3.18
Weight (kg): 0.79