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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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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
Official Date: 7 June 2006
Dates:
DateEvent
7 June 2006Published
Number: No.06-
Number of Pages: 36
Status: Not Peer Reviewed
Access rights to Published version: Open Access

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