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Towards a Theory of Random Numerical Dynamics

In: Stochastic Dynamics

Author

Listed:
  • Peter E. Kloeden
  • Hannes Keller
  • Björn Schmalfuß

Abstract

Random dynamical systems are intrinsically nonautonomous and are formulated in terms of cocycles rather than semigroups. They consequently require generalizations of the commonly used dynamical systems concepts such as attractors and invariance of sets. This cocycle formalism is reviewed here and then the approximation of such dynamical behaviour by time discretized numerical schemes is discussed, outlining results that have been obtained and those that remain to be resolved.

Suggested Citation

  • Peter E. Kloeden & Hannes Keller & Björn Schmalfuß, 1999. "Towards a Theory of Random Numerical Dynamics," Springer Books, in: Stochastic Dynamics, chapter 11, pages 259-282, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-22655-2_11
    DOI: 10.1007/0-387-22655-9_11
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