It has been noted that there are numerous similarities between the behaviour of chaotic and stochastic systems. The theoretical links between chaotic and stochastic systems are investigated based on the evolution of the density of dynamics and an equivalency relationship based on the invariant measure of an ergodic system. It is shown that for simple chaotic systems an equivalent stochastic model can be analytically derived when the initial position in state space is only known to a limited precision. Based on this a new methodology for the modelling of complex nonlinear time series displaying chaotic behaviour with stochastic models is proposed. This consists of using a stochastic model to learn the evolution of the density of the dynamics of the chaotic system by estimating initial and transitional density functions directly from a time series. A number of models utilising this methodology are proposed, based on Markov chains and hidden Markov models. These are implemented and their performance and characteristics compared using computer simulation with several standard techniques.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:399317 |
| Date | January 1999 |
| Creators | Stamp, D. I. |
| Publisher | University of Liverpool |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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