Compatible Measures and Merging
Mathematics of Operations Research, Vol. 21, 1996
Posted: 7 Mar 2012
Date Written: March 7, 2012
Abstract
Two measures, P and Q, are updated as more information arrives. If with P-probability one the predictions of future events according to both measures become close, as time passes, we say that Q merges to P. Blackwell and Dubins [BD] showed that if P is absolutely continuous with respect to Q then Q merges to P. Restricting the definition to prediction of near future events and to a full sequence of times yields the new notion of almost weak merging (AWM), presented here. We introduce a necessary and sufficient condition and show many cases with no absolute continuity that exhibit AWM. We show, for instance, that the fact that Q is diffused around P implies AWM.
Keywords: merging, learning, diffusion
JEL Classification: D83
Suggested Citation: Suggested Citation