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Autocontinuity, convergence in measure, and convergence in distribution

Fuzzy Sets and Systems, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Toshiaki Murofushi   +2 more
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Convergence of Distributions

2016
It is natural to introduce a notion of convergence for sequences of cumulative distribution functions , i.e. to give a meaning to the expression \(F_n\rightarrow F\). One possible meaning could be pointwise convergence, i.e.: \(F_n(x)\rightarrow F(x)\) for every \(x \in \mathbb R\). However this notion of convergence turns out to be too restrictive.
Francesca Biagini, Massimo Campanino
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Convergence in Distribution

2021
Tightness and relative compactness, convergence and tightness in function spaces, convergence of continuous and rcll processes, functional central limit theorem, moments and tightness, optional equi-continuity and tightness, approximation of random walks, tightness and convergence of random measures, existence via tightness, vague and weak convergence,
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Convergence of Distributions

2010
We now introduce a notion of convergence in the linear space\(\mathcal{D}^\prime(X)\) of distributions on an open set X in R n.
J. J. Duistermaat, J. A. C. Kolk
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Convergence of Distributed Power Control

2010 IEEE International Conference on Communications, 2010
The convergence of non-cooperative distributed power control in Gaussian interference channel is analyzed in this paper. Firstly, the existing distributed power control schemes are categorized as two types: gradient projection type and non-linear type, according to the iterative steps.
Qianxi Lu   +3 more
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Convergence in Distribution

2005
This chapter discusses the basic notions of convergence in distribution. Given a sequence of random variables, when do their distributions converge in a useful way to a limit? In statisticians’ language, given a random sample \(X_1, \ldots, X_n,\) the sample mean \(\bar{X}_n\) is CAN; that is, consistent and asymptotically normal.
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On Convergence to the Uniform Distribution

Theory of Probability & Its Applications, 2006
This paper considers sums of independent identically distributed random variables. We give an example in which, under the unbounded growth of a number of summands, the probability densities $\widetilde{p}_n(x)$ of fractional parts of these sums converge to 1 in the sense of $\int_{0}^1\big|\widetilde{p}_n(x)-1\big|\,dx\to 0,$ but they do not converge ...
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