A weak bifurcation theory for discrete time stochastic dynamical systems

Cees Diks () and Florian Wagener

No 06-04, CeNDEF Working Papers from Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance

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 (non-bifurcating) systems is open and dense. The theory is illustrated with some simple examples.

Date: 2006
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Related works:
Working Paper: A Weak Bifurcation Theory for Discrete Time Stochastic Dynamical Systems (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:ams:ndfwpp:06-04

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