Compatible Measures and Merging

Mathematics of Operations Research, Vol. 21, 1996

Posted: 7 Mar 2012

See all articles by Ehud Lehrer

Ehud Lehrer

Tel Aviv University - School of Mathematical Sciences

Rann Smorodinsky

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

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

Lehrer, Ehud and Smorodinsky, Rann, Compatible Measures and Merging (March 7, 2012). Mathematics of Operations Research, Vol. 21, 1996, Available at SSRN: https://ssrn.com/abstract=2017447

Ehud Lehrer

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Rann Smorodinsky (Contact Author)

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Haifa 32000
Israel

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