On MV-Algebraic Versions of the Strong Law of Large Numbers [PDF]
Entropy, 2019 Many-valued (MV; the many-valued logics considered by Łukasiewicz)-algebras are algebraic systems that generalize Boolean algebras. The MV-algebraic probability theory involves the notions of the state and observable, which abstract the probability ...
Piotr Nowak, Olgierd Hryniewicz
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Convergence rates in the law of large numbers for long-range dependent linear processes [PDF]
Journal of Inequalities and Applications, 2017 Baum and Katz (Trans. Am. Math. Soc. 120:108-123, 1965) obtained convergence rates in the Marcinkiewicz-Zygmund law of large numbers. Their result has already been extended to the short-range dependent linear processes by many authors.
Tao Zhang, Pingyan Chen, Soo Hak Sung
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Strong Law of Large Numbers of Pettis-Integrable Multifunctions
Journal of Mathematics, 2019 Using reversed martingale techniques, we prove the strong law of large numbres for independent Pettis-integrable multifunctions with convex weakly compact values in a Banach space.
Hamid Oulghazi, Fatima Ezzaki
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A new proof for the generalized law of large numbers under Choquet expectation
Journal of Inequalities and Applications, 2020 In this article, we employ the elementary inequalities arising from the sub-linearity of Choquet expectation to give a new proof for the generalized law of large numbers under Choquet expectations induced by 2-alternating capacities with mild assumptions.
Jing Chen, Zengjing Chen
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Law of large numbers and central limit theorem for ergodic quantum processes [PDF]
Journal of Mathematics and Physics, 2023 A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving.
Lubashan Pathirana, J. Schenker
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Law of large numbers for the maximum of the two-dimensional Coulomb gas potential [PDF]
Electronic Journal of Probability, 2023 We derive the leading order asymptotics of the logarithmic potential of a two dimensional Coulomb gas at arbitrary positive temperature. The proof is based on precise evaluation of exponential moments, and the theory of Gaussian multiplicative chaos.
Gaultier Lambert +2 more
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On the Necessary and Sufficient Conditions for Peng’s Law of Large Numbers Under Sublinear Expectations [PDF]
Chinese Annals of Mathematics. Series B, 2021 In this paper, the authors firstly establish the weak laws of large numbers on the canonical space (RN,B(RN))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
Xinpeng Li, Gaofeng Zong
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Mean Field Analysis of Neural Networks: A Law of Large Numbers [PDF]
SIAM Journal on Applied Mathematics, 2018 Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks.
Justin A. Sirignano, K. Spiliopoulos
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A strong law of large numbers for scrambled net integration [PDF]
SIAM Review, 2020 This article provides a strong law of large numbers for integration on digital nets randomized by a nested uniform scramble. The motivating problem is optimization over some variables of an integral over others, arising in Bayesian optimization.
A. Owen
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General epidemiological models: law of large numbers and contact tracing [PDF]
Electronic Journal of Probability, 2021 We study a class of individual-based, fixed-population size epidemic models under general assumptions, e.g., heterogeneous contact rates encapsulating changes in behavior and/or enforcement of control measures.
Jean-jil Duchamps +2 more
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