NDLI: On Strongly Equivalent Nonrandomized Transition Probabilities

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Feinberg, E. A. Piunovskiy, A. B.
Copyright Year	2010
Abstract	Dvoretzky, Wald, and Wolfowitz proved in 1951 the existence of equivalent and strongly equivalent mappings for a given transition probability when the number of nonatomic measures is finite and the decision set is finite. This paper introduces a notion of strongly equivalent transition probabilities with respect to a finite collection of functions. This notion contains the notions of equivalent and strongly equivalent transition probabilities as particular cases. This paper shows that a strongly equivalent mapping with respect to a finite collection of functions exists for a finite number of nonatomic distributions and finite decision set. It also provides a condition when this is true for a countable decision set. According to a recent example by Loeb and Sun, a strongly equivalent mapping may not exist under these conditions when the decision set is uncountable. This paper also provides two additional counterexamples and shows that strongly equivalent mappings exist for homogeneous transition probabilities.
Starting Page	300
Ending Page	307
Page Count	8
File Format	PDF
ISSN	0040585X
DOI	10.1137/S0040585X97984255
e-ISSN	10957219
Journal	Theory of Probability & Its Applications (TPRBAU)
Issue Number	2
Volume Number	54
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-05-21
Access Restriction	Subscribed
Subject Keyword	strongly equivalent transition probabilities set of solutions strongly equivalent transition probabilities with respect to a finite functions set nonatomic measure
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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