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INVARIANT PROBABILITY DISTRIBUTIONS IN ECONOMIC MODELS: A GENERAL RESULT

Published online by Cambridge University Press:  10 June 2004

ALFREDO MEDIO
ALFREDO MEDIO
Affiliation:
University Ca' Foscari of Venice
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Abstract

This paper discusses the asymptotic behavior of distributions of state variables of Markov processes generated by first-order stochastic difference equations. It studies the problem in a context that is general in the sense that (i) the evolution of the system takes place in a general state space (i.e., a space that is not necessarily finite or even countable); and (ii) the orbits of the unperturbed, deterministic component of the system converge to subsets of the state space which can be more complicated than a stationary state or a periodic orbit, that is, they can be aperiodic or chaotic. The main result of the paper consists of the proof that, under certain conditions on the deterministic attractor and the stochastic perturbations, the Markov process describing the dynamics of a perturbed deterministic system possesses a unique, invariant, and stochastically stable probability measure. Some simple economic applications are also discussed.

Keywords

Stochastic StabilityMarkov ProcessesChaotic DynamicsSunspots
Type
Research Article
Information
Macroeconomic Dynamics , Volume 8 , Issue 2 , April 2004 , pp. 162 - 187
Copyright
© 2004 Cambridge University Press

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