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The strong convergence of maximal degrees in uniform random recursive trees and dags

Random Structures & Algorithms, 1995
AbstractWe show that the maximal degree in a uniform random recursive tree is almost surely (1 + o(1)) log2n. A random directed acyclic graph on n nodes is defined by connecting the ith node for each i > m with r of its predecessors uniformly and at random. The maximal degree is shown to be almost surely (1 + o(1))log1+1/rn.
Dovroye, Luc, Lu, Jiang
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Rates of strong uniform convergence of the k T -occupation time density estimator

Statistical Inference for Stochastic Processes, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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NECESSARY CONDITION FOR THE STRONG UNIFORM CONVERGENCE OF THE NEAREST NEIGHBOUR DENSITY ESTIMATE

Acta Mathematica Scientia, 1984
The present paper is concerned with the problem of whether strong uniform consistency of nearest neighbour density estimates necessarily entails uniform continuity of the underlying density (from the author's introduction).
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Law of convergence of strong cylindrical and spherical shock waves in a gas with a uniform density

JETP Letters, 2015
A model of convergence of cylindrical and spherical shock waves in a gas with a uniform density has been considered. The partial differential equations of this model have been reduced to ordinary differential equations, from which the laws of convergence of such shock waves and the dependence α = f(γ, M) of their self-similarity index α on the heat ...
U. Yusupaliev   +3 more
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A strong uniform convergence rate of kernel conditional quantile estimator under random censorship

Statistics & Probability Letters, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Strong uniform convergence of composition sequences of probability measures on locally compact topological semigroups

Science in China Series A: Mathematics, 1997
Let \(S\) be a locally compact topological semigroup and \(\{\mu_n,\;n=1,2,\dots\}\) a sequence of probability measures on \(S\). Consider the convolution \(\mu_{k+1}*\mu_{k+2}*\cdots* \mu_n\) by \(\mu_{k,n}\) and assume further that \(\{\mu_{k,n},\;k=1,2,\dots,k< n\}\) is a tight set of probability measures.
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Rates of strong uniform convergence of nearest neighbor density estimates on any compact set

Applied Mathematics and Mechanics, 1990
Strong uniform convergence rates of univariate nearest neighbor density estimators on compact sets are considered under various conditions.
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A new wavelet estimator of multivariate copula densities based on Sklar's theorem, with optimal strong uniform convergence rate

South African Statistical Journal
In this paper, we propose a natural wavelet estimator of multivariate copula densities as a ratio of the linear wavelet estimator of the underlying joint population density function and the product of the linearwavelet estimators of the corresponding marginal density functions.
Swanepoel, Jan   +2 more
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