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April, 1991 Unstable Collectives and Envelopes of Probability Measures
Adrian Papamarcou, Terrence L. Fine
Ann. Probab. 19(2): 893-906 (April, 1991). DOI: 10.1214/aop/1176990457


We discuss issues of existence and stochastic modeling in regard to sequences that exhibit combined features of independence and instability of relative frequencies of marginal events. The concept of independence used here is borrowed from the frequentist account of numerical probability advanced by von Mises: A sequence is independent if certain salient asymptotic properties are invariant under the causal selection of subsequences. We show that independence (in the above sense) and instability of relative frequency are indeed compatible and that sequences with such features support stochastic models expressed in terms of envelopes of probability measures.


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Adrian Papamarcou. Terrence L. Fine. "Unstable Collectives and Envelopes of Probability Measures." Ann. Probab. 19 (2) 893 - 906, April, 1991.


Published: April, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0727.60004
MathSciNet: MR1106292
Digital Object Identifier: 10.1214/aop/1176990457

Primary: 60G05
Secondary: 60A05

Keywords: frequentist probability , independence , interval-valued probability , subsequence selections , unstable relative frequencies , upper and lower envelopes , Upper and lower probability , von Mises collectives

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • April, 1991
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