Diks, Cees and Wagener, Florian O. O. (2006) A weak bifucation theory for discrete time stochastic dynamical systems. Working Paper. Warwick Business School, Financial Econometrics Research Centre, Coventry.

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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 (nonbifurcating) systems is open and dense. The theory is illustrated with some simple examples.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre Faculty of Social Sciences > Warwick Business School
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
Date:	7 June 2006
Number:	No.06-
Number of Pages:	36
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/1754

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