Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2006-05-09
Number: 06-043/1
Author-Name: Cees Diks
Author-Email: C.G.H.Diks@uva.nl
Author-Workplace-Name: CeNDEF, Universiteit van Amsterdam
Author-Name: Florian Wagener
Author-Email: f.o.o.wagener@uva.nl
Author-Workplace-Name: CeNDEF, Universiteit van Amsterdam
Title: A Weak Bifurcation Theory for Discrete Time Stochastic Dynamical Systems
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.
Classification-JEL: C14; C22; C32
Keywords: stochastic bifurcation theory
File-Url: https://papers.tinbergen.nl/06043.pdf
File-Format: application/pdf
File-Size: 1110419 bytes
Handle: RePEc:tin:wpaper:20060043