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2021
Abstract This chapter reviews the theory of weak convergence in metric spaces. Topics include Skorokhod’s representation theorem, the metrization of spaces of measures, and the concept of tightness of probability measures. The key relation is shown between weak convergence and uniform tightness.
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Abstract This chapter reviews the theory of weak convergence in metric spaces. Topics include Skorokhod’s representation theorem, the metrization of spaces of measures, and the concept of tightness of probability measures. The key relation is shown between weak convergence and uniform tightness.
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1998
Abstract We denote the weak partial derivatives of u and the weak gradient of u by respectively. We adopt the usual notation The following properties hold for weak converging sequences.
Andrea Braides, Anneliese Defranceschi
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Abstract We denote the weak partial derivatives of u and the weak gradient of u by respectively. We adopt the usual notation The following properties hold for weak converging sequences.
Andrea Braides, Anneliese Defranceschi
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Approximation of Weak Convergence
Mathematische Nachrichten, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Weak Convergence of Random Sums
Theory of Probability & Its Applications, 2002The authors prove various limit theorems for sums of a random number of independent random variables. Throughout, the number of variables is independent of the summands themselves.
Kruglov, V. M., Zhang, Bo
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Weak Convergence: Introduction
1997Up to now, we have concentrated on the convergence of {θ n } or of {θ n (·)} to an appropriate limit set with probability one. In this chapter, we work with a weaker type of convergence. In practical applications, this weaker type of convergence most often yields exactly the same information about the asymptotic behavior as the probability one methods.
Harold J. Kushner, G. George Yin
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On Weak Convergence of Hypermeasures
Mathematische Nachrichten, 1984AbstractMeasures on the hyperspace of the closed sets with the FLACHSMEYER‐FELL topology are completely defined by their capacities. A necessary and sufficient condition is given for the weak convergence of a sequence of positive bounded σ‐additive measures on the hyperspace in terms of their capacities.
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Strong Convergence and Weak Convergence
1965In this chapter, we shall be concerned with certain basic facts pertaining to strong-, weak- and weak* convergences, including the comparison of the strong notion with the weak notion, e.g., strong- and weak measurability, and strong- and weak analyticity.
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