Wasserstein-p bounds in the central limit theorem under local dependence [PDF]
Electronic Journal of Probability, 2023 The central limit theorem (CLT) is one of the most fundamental results in probability; and establishing its rate of convergence has been a key question since the 1940s.
Tianle Liu, Morgane Austern
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KOLMOGOROV BOUNDS FOR THE NORMAL APPROXIMATION OF THE NUMBER OF TRIANGLES IN THE ERDŐS–RÉNYI RANDOM GRAPH [PDF]
Probability in the engineering and informational sciences (Print), 2017 We bound the error for the normal approximation of the number of triangles in the Erdős–Rényi random graph with respect to the Kolmogorov metric. Our bounds match the best available Wasserstein bounds obtained by Barbour et al. [(1989).
Adrian Röllin
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Average Characteristic Polynomials of Determinantal Point Processes [PDF]
, 2015 We investigate the average characteristic polynomial $\mathbb E\big[\prod_{i=1}^N(z-x_i)\big] $ where the $x_i$'s are real random variables which form a determinantal point process associated to a bounded projection operator.
Hardy, Adrien
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Uniform convergence rates and uniform adaptive estimation in mixtures of regressions [PDF]
, 2018 In this thesis, we develop theoretical tools to examine estimators in non-parametric regression models in regard of uniform convergence rates and uniform adaptivity with respect to the smoothness of the parameter functions.
Werner, Heiko
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Acknowledgement of Priority “Weighted Averages of Random Variables and Exact Weights”
, 2014 During preparation of the manuscript, the authors were not aware of a number of papers devoted to so-called exact strong laws of large numbers. Professor André Adler turned our attention to his results on this problem (see [1], [2], [3], where further ...
P. Matuła, M. Seweryn
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Convergence of discrete time Kalman filter estimate to continuous time estimate [PDF]
, 2015 This article is concerned with the convergence of the state estimate obtained from the discrete time Kalman filter to the continuous time estimate as the temporal discretization is refined.
Aalto, Atte
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Weak Convergence in the Prokhorov Metric of Methods for Stochastic Differential Equations
, 2008 We consider the weak convergence of numerical methods for stochastic differential equations (SDEs). Weak convergence is usually expressed in terms of the convergence of expected values of test functions of the trajectories. Here we present an alternative
Benoit Charbonneau +3 more
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Information Ranking and Power Laws on Trees [PDF]
, 2010 We study the situations when the solution to a weighted stochastic recursion has a power law tail. To this end, we develop two complementary approaches, the first one extends Goldie's (1991) implicit renewal theorem to cover recursions on trees; and the ...
Jelenkovic, Predrag R. +1 more
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Proof mining and probability theory
Forum of Mathematics, SigmaWe extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie “noncomputational” proofs from probability theory, thereby unlocking ...
Morenikeji Neri, Nicholas Pischke
doaj +1 more source
Convergence Vague (IA) - Suites de vecteurs Aléatoires [PDF]
, 2016 This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary foundation that paves the
Gane Samb Lo
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