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On the computation of invariant measures in random dynamical systems

Please always quote using this URN:urn:nbn:de:0296-matheon-486
  • Invariant measures of dynamical systems generated e. g. by difference equations can be computed by discretizing the originally continuum state space, and replacing the action of the generator by the transition mechanism of a Markov chain. In fact they are approximated by stationary vectors of these Markov chains. Here we extend this well known approximation result and the underlying algorithm to the setting of random dynamical systems, i.e. dynamical systems on the skew product of a probability space carrying the underlying stationary stochasticity and the state space, a particular non-autonomous framework. The systems are generated by difference equations driven by stationary random processes modelled on a metric dynamical system. The approximation algorithm involves spatial discretizations and the definition of appropriate random Markov chains with stationary vectors converging to the random invariant measure of the system.

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Metadaten
Author:Peter Imkeller, Peter Kloeden
URN:urn:nbn:de:0296-matheon-486
Referee:Anton Bovier
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2004/01/19
Release Date:2004/01/15
Institute:Humboldt-Universität zu Berlin
Preprint Number:45
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