A Limit Theorem for the Prediction Process under Absolute Continuity

Hideatsu Tsukahara

No 97-F-34, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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 (1962) 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.

Pages: 8 pages
Date: 1997-10
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