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A weak bifucation theory for discrete time stochastic dynamical systems
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Diks, Cees and Wagener, Florian O. O. (2006) A weak bifucation theory for discrete time stochastic dynamical systems. Working Paper. Coventry: Warwick Business School, Financial Econometrics Research Centre. Working papers (Warwick Business School. Financial Econometrics Research Centre) (No.06-).
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Official URL: http://www2.warwick.ac.uk/fac/soc/wbs/research/wfr...
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 (nonbifurcating) systems is open and dense. The theory is illustrated with some simple examples.
Item Type: | Working or Discussion Paper (Working Paper) | ||||
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Subjects: | H Social Sciences > HB Economic Theory Q Science > QA Mathematics |
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Divisions: | Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre Faculty of Social Sciences > Warwick Business School |
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Library of Congress Subject Headings (LCSH): | Bifurcation theory, Differential equations, Nonlinear -- Numerical solutions, Dependence (Statistics), Stochastic difference equations | ||||
Series Name: | Working papers (Warwick Business School. Financial Econometrics Research Centre) | ||||
Publisher: | Warwick Business School, Financial Econometrics Research Centre | ||||
Place of Publication: | Coventry | ||||
Official Date: | 7 June 2006 | ||||
Dates: |
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Number: | No.06- | ||||
Number of Pages: | 36 | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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