Positive dependence and weak convergence

Marco Scarsini (1, 2) , A. Colangelo , A. Müller

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 Dipartimento di Scienze Economiche e Aziendali

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.

Mots clés: Affiliation; MTP_2; conditionally increasing in sequence; conditionally increasing

Domaines: Economie et sciences de la décision

Marco Scarsini, A. Colangelo, A. Müller. Positive dependence and weak convergence. Journal of Applied Probability, 2006, Vol. 43, N°1, pp.48-59. ⟨10.1239/jap/1143936242⟩. ⟨hal-00539004⟩