A weak bifurcation theory for discrete time stochastic dynamical systems
AbstractThis 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 InfoPaper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 06-04.
Date of creation: 2006
Date of revision:
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Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
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Other versions of this item:
- Cees Diks & Florian Wagener, 2006. "A Weak Bifurcation Theory for Discrete Time Stochastic Dynamical Systems," Tinbergen Institute Discussion Papers 06-043/1, Tinbergen Institute.
- Florian Wagener & Cees Diks, 2006. "A weak bifucation theory for discrete time stochastic dynamical systems," Working Papers wp06-14, Warwick Business School, Financial Econometrics Research Centre.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
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- 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.
- 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, vol. 7(2), pages 263-276.
- 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, vol. 35(1), pages 148-162, January.
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