Weak Convergence of Probability Measures

Topics in weak convergence of probability measures

The first part of the paper deals with general features of weak star convergence from a topological point of view. We present basic facts about weak and weak star topologies, dual spaces and representations of linear functionals as Radon measures. A special attention is payed to finitely additive measures and some results regarding the Baire sets. We prove that in a wide class of topological sp...

Weak Convergence of Random Sets

In this paper the classical Portmanteau theorem which provides equivalent conditions of weak convergence of sequence of probability measures is extended on the space of the sequence of probability measures induced by random sets.

2 00 6 Portmanteau theorem for unbounded measures

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element. 2000 Mathematics Subject Classification: 60B10, 28A33

Weak Convergence of Convolution Products of Probability Measures on Semihypergroups

Let S be a topological semihypergroup. As it is known for hypergroups, the lack of an algebraic structure on a semihypergroup pause a serious challenge in extending results from semigroups. We use the notion of concretization or pseudomultiplication, to prove some results on weak convergence of the sequence of averages of convolution powers of probability measures on topological semihypergroups...

A dissertation under the direction of Gordon Simons . SOME STRUCTURAL RELATIONSHIPS BETWEEN WEAK CONVERGENCE OF PROBABILITY MEASURES AND CONVERGENCE IN PROBABILITY Flav

Convergence of Probability Measures and Markov Decision Models with Incomplete Information

This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise convergence, and convergence in total variation. First, it describes and compares necessary and sufficient conditions for these types of convergence, some of which are well-known, in terms of convergence of probabilities of open and closed sets and, for the probabilities on...