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A Weak Bifurcation Theory for Discrete Time Stochastic Dynamical Systems


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  • Cees Diks

    (CeNDEF, Universiteit van Amsterdam)

  • Florian Wagener

    (CeNDEF, Universiteit van Amsterdam)


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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Bibliographic Info

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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Keywords: stochastic bifurcation theory;

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  1. Igor V. Evstigneev & Michal A. H. Dempster & Klaus R. Schenk-Hoppé, 2003. "Exponential growth of fixed-mix strategies in stationary asset markets," Finance and Stochastics, Springer, Springer, vol. 7(2), pages 263-276.
  2. Saralees Nadarajah & Kosto Mitov & Samuel Kotz, 2003. "Local dependence functions for extreme value distributions," Journal of Applied Statistics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 30(10), pages 1081-1100.
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Cited by:
  1. Chiarella, Carl & He, Xue-Zhong & Zheng, Min, 2011. "An analysis of the effect of noise in a heterogeneous agent financial market model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 35(1), pages 148-162, January.


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