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Almost sure weak convergence of random probability measures

Stochastics, 2006
Given a sequence (μ n ) of random probability measures on a metric space S, consider the conditions: (i) μ n →μ (weakly) a.s. for some random probability measure μ on S; (ii) μ n (f) converges a.s. for all f∈C b (S). Then, (i) implies (ii), while the converse is not true, even if S is separable. For (i) and (ii) to be equivalent, it is enough that S is
Patrizia Berti, Luca Pratelli, Pietro Rigo   +2 more
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On the Weak Convergence of Probability Measures in Orlicz Spaces

Theory of Probability and Its Applications, 1996
Necessary and sufficient conditions for weak convergence of probability measures in separable Orlicz spaces in terms of characteristic functionals and norm moments are given.
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On weak convergence of probability measures, channel capacity and code error probabilities

IEEE Transactions on Information Theory, 1996
Let \({\mathcal X}\) be the possibly infinite set of channel inputs and \({\mathcal Y}\) the output alphabet where \({\mathcal Y}\) is the Borel \(\sigma\)-field of a separable metric space \(({\mathcal Y},d)\). A channel \({\mathcal C}\) is a family of probability measures on \({\mathcal Y}\), i.e., \({\mathcal C}=(P^x)_{x\in{\mathcal X}}\) where \(P ...
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Weak convergence of measures

Mathematische Annalen, 1971
Helmut H Schaefer, Schaefer Helmut H
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A note on the weak convergence of probability measures in the D[0,1] space

Statistics and Probability Letters, 2008
Abstract Let τ be a regular metric as defined below for the D = D [ 0 , 1 ] space. Even when ( D , τ ) is not a separable and complete metric space we show (i) that the usual conditions on a sequence of probability measures in ( D , τ ) ensures its weak convergence and (ii) that Prohorov's theorem in ( D , τ ) can
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Weak Convergence of Probability Measures

1978
The methods of the theory of weak convergence of probability measures are of wide use in many areas of applications to statistics, operations research and stochastic control theory, where it is convenient or useful to approximate a process by a sequence of other processes or vice versa.
Harold J. Kushner, Dean S. Clark
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On Weak Convergence of Probability Measures in a Banach Space

Journal of Mathematical Sciences, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Weak Convergence of Probability Measures

2013
Let X = (X1, X2,…, X p ) be a p-vector variable with df \( \mathbb{F} \) and dm denoted by µ X or µF. The df F j of X j is called the j th marginal of X or of \( \mathbb{F} \) or of µF, 1 ≤ j ≤ p.
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FUZZY CONVERGENCE VERSUS WEAK CONVERGENCE IN SPACES OF PROBABILITY MEASURES

1984
If X is a separable metrizable space, then on the set \({\mathcal M}(X)\) of all probability measures on X, the structure most frequently used is the weak topology, also called topology of weak convergence. In Math. Nachr. 115, 33-57 (1984; Zbl 0593.54006), the author introduced an alternative structure, a fuzzy topology, the topological modification ...
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Weak Convergence of Probability Measures

1977
Throughout this chapter we shall concern ourselves with the study of probability measures on separable metric spaces only. As usual, for any such metric space X we shall write B X for the borel σ-algebra of subsets of X. We shall denote by C(X) the space of all bounded real valued continuous functions on X and M0(X) the space of all probability ...
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