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 Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-043/1.
Date of creation: 09 May 2006
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stochastic bifurcation theory;
Other versions of this item:
- Florian Wagener & Cees Diks, 2006. "A weak bifucation theory for discrete time stochastic dynamical systems," Working Papers wp06-14, Warwick Business School, Finance Group.
- Diks, C.G.H. & Wagener, F.O.O., 2006. "A weak bifurcation theory for discrete time stochastic dynamical systems," CeNDEF Working Papers 06-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- 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 &bull Diffusion Processes
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
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- 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.
- Saralees Nadarajah & Kosto Mitov & Samuel Kotz, 2003. "Local dependence functions for extreme value distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1081-1100.
- 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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