Stochastic Dynamics

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

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Hardcover | 26 March 1999

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472 Pages

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24.13 x 15.88 x 3.18

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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.

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Probability & Statistics Calculus & Mathematical Analysis Optimisation

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

Stochastic Dynamics

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Hardcover

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