A weak bifucation theory for discrete time stochastic dynamical systems
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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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|
|Number of Pages:||36|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
 I.S. Abramson, On bandwidth variation in kernel estimates - a square root law, Annals of Statistics 10 (1982), 1217–1223.
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