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Positive Dependence and Weak Convergence

Part of: Distribution theory - Probability Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  14 July 2016

A. Colangelo ,
A. Müller  and
M. Scarsini
A. Colangelo*
Affiliation:
Università dell'Insubria
A. Müller*
Affiliation:
Universität Karlsruhe
M. Scarsini*
Affiliation:
Università di Torino
*
∗ Postal address: Dipartimento di Economia, Università dell'Insubria, Via Monte Generoso 71, I-21100 Varese, Italy. Email address: antonio.colangelo@uninsubria.it
∗∗ Postal address: Institut für Wirtschaftstheorie und Operations Research, Universität Karlsruhe, Geb. 20.21, D-76128 Karlsruhe, Germany. Email address: mueller@wior.uni-karlsruhe.de
∗∗∗ Postal address: Dipartimento di Statistica e Matematica Applicata, Università di Torino, Piazza Arbarello 8, I-10122 Torino, Italy. Email address: marco.scarsini@unito.it
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Abstract

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A more general definition of MTP2 (multivariate total positivity of order 2) probability measure is given, without assuming the existence of a density. Under this definition the class of MTP2 measures is proved to be closed under weak convergence. Characterizations of the MTP2 property are proved under this more general definition. Then a precise definition of conditionally increasing measure is provided, and closure under weak convergence of the class of conditionally increasing measures is proved. As an application we investigate MTP2 properties of stationary distributions of Markov chains, which are of interest in actuarial science.

Keywords

AffiliationMTP2conditionally increasing in sequenceconditionally increasing

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60B10: Convergence of probability measures
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 48 - 59
Copyright
© Applied Probability Trust 2006 

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