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On Some Topological Properties of Stable Measures

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  • Nielsen, Carsten Krabbe

Abstract

The paper shows that the set of stable probability measures and the set of Rational Beliefs relative to a given stationary measure are closed in the strong topology but not closed in the topology of weak convergence. However, subsets of the set of stable probability measures which are characterized by uniformity of convergence of the empirical distribution are closed in the topology of weak convergence. It is demonstrated that such subsets exist. In particular, there is an increasing sequence of sets of SIDS measures who's union is the set of all SIDS measures generated by a particular system and such that each subset consists of stable measures. The uniformity requirement has a natural interpretation in terms of plausibility of Rational Beliefs.

Suggested Citation

  • Nielsen, Carsten Krabbe, 1996. "On Some Topological Properties of Stable Measures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 531-553, October.
    • Handle: RePEc:spr:joecth:v:8:y:1996:i:3:p:531-53
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    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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