This article is cited in 7 papers

Generalization of Portmanteau Theorem with Respect to the Pseudoweak Convergence of Random Closed Sets

T. Grbić, E. Pap

University of Novi Sad

Abstract: The main result of this paper is a theorem of portmanteau type for pseudoweak convergent sequences of capacity functionals for a sequence of random closed sets. For that purpose the classical Lebesgue integral had been substituted with a more general one, known as general pseudo-integral, and there is introduced the pseudoweak convergence of capacity functionals. A connection between weak convergence of a sequence of probability measures induced by the sequence of random closed sets and convergence of pseudo-integral with respect to the corresponding sequence of capacity functionals is given.

Keywords: portmanteau theorem, pseudo-operations, pseudo-integral, random closed set, capacity functional, pseudoweak convergence.

Received: 08.10.2007

Language: English

DOI: 10.4213/tvp2548

 English version: Theory of Probability and its Applications, 2010, 54:1, 51–67

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