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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)

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:

Date	Event
7 June 2006	Published

Number:

No.06-

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

References:

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URI:

http://wrap.warwick.ac.uk/id/eprint/1754

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