A Weak Bifurcation Theory for Discrete Time Stochastic Dynamical Systems

Cees Diks () and Florian Wagener
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Cees Diks: CeNDEF, Universiteit van Amsterdam

No 06-043/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: stochastic; bifurcation; theory (search for similar items in EconPapers)
JEL-codes: C14 C22 C32 (search for similar items in EconPapers)
Date: 2006-05-09
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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:tin:wpaper:20060043

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