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Stochastic Dynamics

  • Book
  • © 1999

Overview

Authors:
  1. Hans Crauel

    1. FB 3 Mathematik, Sekr. MA 7-4, TU Berlin, Berlin, Germany

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  2. Matthias Gundlach

    1. Institute für Dynamische Systeme, Universität Bremen, Bremen, Germany

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xxvii
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  2. Stability Along Trajectories at a Stochastic Bifurcation Point

    • Peter H. Baxendale
    Pages 1-25

  3. Bifurcations of One-Dimensional Stochastic Differential Equations

    • Hans Crauel, Peter Imkeller, Marcus Steinkamp
    Pages 27-47

  4. P-Bifurcations in the Noisy Duffing-van der Pol Equation

    • Yan Liang, N. Sri Namachchivaya
    Pages 49-70

  5. The Stochastic Brusselator: Parametric Noise Destroys Hoft Bifurcation

    • Ludwig Arnold, Gabriele Bleckert, Klaus Reiner Schenk-Hoppé
    Pages 71-92

  6. Numerical Approximation of Random Attractors

    • Hannes Keller, Gunter Ochs
    Pages 93-115

  7. Random Hyperbolic Systems

    • Volker Matthias Gundlach, Yuri Kifer
    Pages 117-145

  8. Some Questions in Random Dynamical Systems Involving Real Noise Processes

    • Russell Johnson
    Pages 147-180

  9. Topological, Smooth, and Control Techniques for Perturbed Systems

    • Fritz Colonius, Wolfgang Kliemann
    Pages 181-208

  10. Perturbation Methods for Lyapunov Exponents

    • Volker Wihstutz
    Pages 209-239

  11. The Lyapunov Exponent of the Euler Scheme for Stochastic Differential Equations

    • Denis Talay
    Pages 241-258

  12. Towards a Theory of Random Numerical Dynamics

    • Peter E. Kloeden, Hannes Keller, Björn Schmalfuß
    Pages 259-282

  13. Canonical Stochastic Differential Equations based on Lévy Processes and Their Supports

    • Hiroshi Kunita
    Pages 283-304

  14. On the Link Between Fractional and Stochastic Calculus

    • Martina Zähle
    Pages 305-325

  15. Asymptotic Curvature for Stochastic Dynamical Systems

    • Michael Cranston, Yves Le Jan
    Pages 327-338

  16. Stochastic Analysis on (Infinite-Dimensional) Product Manifolds

    • Sergio Albeverio, Alexei Daletskii, Yuri Kondratiev
    Pages 339-369

  17. Evolutionary Dynamics in Random Environments

    • Lloyd Demetrius, Volker Matthias Gundlach
    Pages 371-394

  18. Microscopic and Mezoscopic Models for Mass Distributions

    • Peter Kotelenez
    Pages 395-431

  19. Back Matter

    Pages 432-440
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Keywords

About this book

The conference on Random Dynamical Systems took place from April 28 to May 2, 1997, in Bremen and was organized by Matthias Gundlach and Wolfgang Kliemann with the help of th'itz Colonius and Hans Crauel. It brought together mathematicians and scientists for whom mathematics, in particular the field of random dynamical systems, is of relevance. The aim of the conference was to present the current state in the theory of random dynamical systems (RDS), its connections to other areas of mathematics, major fields of applications, and related numerical methods in a coherent way. It was, ho~vever, not by accident that the conference was centered around the 60th birthday of Ludwig Arnold. The theory of RDS o~ves much of its current state and status to Ludwig Arnold. Many aspects of the theory, a large number of results, and several substantial contributions were accomplished by Ludwig Arnold. An even larger number of contributions has been initiated by him. The field be- fited much from his enthusiasm, his openness for problems not completely aligned with his o~vn research interests, his ability to explain mathematics to researchers from other sciences as well as his ability to get mathema- clans interested in problems from applications not completely aligned with their research interests. In particular, a considerable part of the impact stochastics had on physical chemistry as well as on engineering goes back to Ludwig Arnold. He built up an active research group, kno~vn as "the Bremen group".

Authors and Affiliations

  • FB 3 Mathematik, Sekr. MA 7-4, TU Berlin, Berlin, Germany

    Hans Crauel

  • Institute für Dynamische Systeme, Universität Bremen, Bremen, Germany

    Matthias Gundlach

Bibliographic Information

  • Book Title: Stochastic Dynamics

  • Authors: Hans Crauel, Matthias Gundlach

  • DOI: https://doi.org/10.1007/b97846

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Hardcover ISBN: 978-0-387-98512-1Published: 26 March 1999

  • Softcover ISBN: 978-1-4757-7266-1Published: 22 April 2013

  • eBook ISBN: 978-0-387-22655-2Published: 14 December 2007

  • Edition Number: 1

  • Number of Pages: XXVII, 440

  • Number of Illustrations: 3 illustrations in colour

  • Topics: Probability Theory and Stochastic Processes, Calculus of Variations and Optimal Control; Optimization

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