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A Weak Bifurcation Theory for Discrete Time Stochastic Dynamical Systems

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Author Info
Cees Diks () (CeNDEF, Universiteit van Amsterdam)
Florian Wagener () (CeNDEF, Universiteit van Amsterdam)

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Abstract

This article presents a bifurcation theory of smooth stochastic dynamical systems that are governed by everywhere positive transition densities. The local dependence structure of the unique strictly stationary evolution of such a system can be expressed by the ratio of joint and marginal probability densities; this 'dependence ratio' is a geometric invariant of the system. By introducing a weak equivalence notion of these dependence ratios, we arrive at a bifurcation theory for which in the compact case, the set of stable (non-bifurcating) systems is open and dense. The theory is illustrated with some simple examples.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-043/1.

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Date of creation: 09 May 2006
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Handle: RePEc:dgr:uvatin:20060043

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Related research
Keywords: stochastic bifurcation theory

Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models

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  1. Saralees Nadarajah & Kosto Mitov & Samuel Kotz, 2003. "Local dependence functions for extreme value distributions," Journal of Applied Statistics, Taylor and Francis Journals, vol. 30(10), pages 1081-1100, December. [Downloadable!] (restricted)
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