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A limit theorem for the prediction process under absolute continuity

  • Hideatsu Tsukahara
Autres Exposés
Part of the Lecture Notes in Mathematics book series (LNM, volume 1709)

Abstract

Consider a stochastic process with two probability laws, one of which is absolutely continuous with respect to the other. Under each law, we look at a process consisting of the conditional distributions of the future given the past. Blackwell and Dubins showed in discrete case that those conditional distributions merge as we observe more and more; more precisely, the total variation distance between them converges to 0 a.s. In this paper we prove its extension to continuous time case using the prediction process of F. B. Knight.

Keywords

Conditional Distribution Absolute Continuity Prediction Process Optional Projection Total Variation Distance 
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References

  1. Blackwell, D. and Dubins, L. (1962). Merging of opinions with increasing information, Ann. Math. Statist. 33, 882–886.MathSciNetCrossRefzbMATHGoogle Scholar
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Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Hideatsu Tsukahara

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