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A weak bifucation theory for discrete time stochastic dynamical systems

By Cees Diks and Florian O. O. Wagener

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

Topics: HB, QA
Publisher: Warwick Business School, Financial Econometrics Research Centre
Year: 2006
OAI identifier: oai:wrap.warwick.ac.uk:1754

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