Randomness in deterministic difference equations

Self-stochasticity theory, established for certain classes of deterministic finite-dimensional dynamical systems, is extended to the continuous time difference equations with and f being continuous interval map. For such equations, self-stochasticity lies in the existence of eventually unpredictable...

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Bibliographic Details
Published in:Journal of difference equations and applications 2010-02, Vol.16 (2-3), p.243-268
Main Author: Romanenko, E.Yu
Format: Article
Language:English
Subjects:
difference equation
Difference equations
Differential equations
Dynamical systems
finite-dimensional distribution
gradient catastrophe
intermixing
Intervals
invariant measure
Mathematical analysis
random function
Randomness
sensitive dependence on initial data
Stochastic models
Stochastic processes
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Summary:Self-stochasticity theory, established for certain classes of deterministic finite-dimensional dynamical systems, is extended to the continuous time difference equations with and f being continuous interval map. For such equations, self-stochasticity lies in the existence of eventually unpredictable solutions (as smooth as desired) whose long-term behaviour is described with some stochastic processes.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236190902766843