Results 221 to 230 of about 56,903 (265)

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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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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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

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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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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A note on convergence of probability measures

Journal of Applied Probability, 2001
We present, discuss and prove an apparently unfamiliar result in the convergence of probability measures.
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On the Convergence in Probability of Random Sets (Measurable Multifunctions)

Mathematics of Operations Research, 1986
It is shown that the convergence in probability of random sets introduced by Salinetti and Wets is consistent with the more standard definitions of convergence in probability, and is metric invariant.
Salinetti, G., Vervaat, W., Wets, R. J.-B.   +2 more
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On “predictable” convergence criteria in variation of probability measures

Russian Mathematical Surveys, 1984
This is an announcement of the results published later with the proofs in the author's paper ''On necessary and sufficient conditions for convergence of probability measures in variation''. Stochastic Processes Appl. 18, 99-112 (1984; Zbl 0547.60008).
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Convergence of Convolution Sequences of Probability Measures

1977
The study of the convergence of sequences of probability measures on a locally compact group is basic for the development of the central limit theorem. This chapter serves as a source of preparatory material as well as a presentation of the smooth part of the theory.
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Weak Convergence of Probability Measures Revisited

1987
The hypo-convergence of upper semicontinuous functions provides a natural framework for the study of the convergence of probability measures. This approach also yields some further characterizations of weak convergence and tightness.
Salinetti, G., Wets, R.J.-B.
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