A bifurcation theory for a class of discrete time Markovian stochastic systems |
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Authors: | CGH Diks FOO Wagener |
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Institution: | Center for Nonlinear Dynamics in Economics and Finance (CeNDEF), Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands |
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Abstract: | We present 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 an equivalence relation defined on these dependence ratios, we arrive at a bifurcation theory for which in the compact case, the set of stable, i.e. non-bifurcating, systems is open and dense. The theory is illustrated with some simple examples. |
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Keywords: | 02 50 -r 05 45-a |
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