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A note on the weak convergence of probability measures in the D[0,1] space
Statistics and Probability Letters, 2008Abstract 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
1978The 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, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Weak Convergence of Probability Measures
1977Throughout 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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Weak Convergence of Probability Measures
2013Let 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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Weak Convergence of Probability Measures on Metric Spaces
2016Let \((S,\rho )\) be a metric space and let \(\mathcal {P}(S)\) be the set of all probability measures on \((S, \mathcal {B}(S)).\) In this chapter we consider a general formulation of convergence in \(\mathcal {P}(S)\), referred to as weak convergence or convergence in distribution.
Rabi Bhattacharya, Edward C. Waymire
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FUZZY CONVERGENCE VERSUS WEAK CONVERGENCE IN SPACES OF PROBABILITY MEASURES
1984If 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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Semigroup Forum, 2004
Let \(S\) be a completely simple semigroup with a given Rees product structure \(A\times B\times C\). A subsemigroup of \(S\) is called a product subsemigroup if it can be represented in a way compatible with the product structure. The authors give conditions under which a subsemigroup of \(S\) is such a product subsemigroup. The area of application of
Budzban, Gregory, Mukherjea, Arunava
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Let \(S\) be a completely simple semigroup with a given Rees product structure \(A\times B\times C\). A subsemigroup of \(S\) is called a product subsemigroup if it can be represented in a way compatible with the product structure. The authors give conditions under which a subsemigroup of \(S\) is such a product subsemigroup. The area of application of
Budzban, Gregory, Mukherjea, Arunava
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Weak Convergence of Probability Measures on Rp and C[0,1]
1995The purpose of this appendix is to explain the concept of weak convergence on C[0,1], the space of continuous functions on the unit interval [0,1]. It explains what is behind the formulae involving Brownian motion and stochastic integrals, which appear in the discussion of the limit distributions in cointegration theory.
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