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On the Law of Large Numbers for Nonidentically Distributed Weakly Dependent Summands
Theory of Probability & Its ApplicationsThree versions of the Weak Law of Large Numbers are proposed for weakly dependent and generally speaking non-equally distributed random variables, with finite or possibly infinite expectations.
A. Akhmiarova, A. Veretennikov
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The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences
Journal of theoretical probability, 2019This paper establishes complete convergence for weighted sums and the Marcinkiewicz–Zygmund-type strong law of large numbers for sequences of negatively associated and identically distributed random variables {X,Xn,n≥1}\documentclass[12pt]{minimal ...
Anh Thi Ngoc Vu +3 more
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The SAGE Encyclopedia of Research Design, 2017 U ovome radu bavit ćemo se uvjetima uz koje nizovi slučajnih varijabli konvergiraju, brzini i vjerojatnosti konvergencije. Najprije ćemo ponoviti osnovne pojmove iz vjerojatnosti, kao što su nezavisnost slučajnih varijabli, matematičko očekivanje i ...
S. Cooper
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Marcinkiewicz’s strong law of large numbers for nonlinear expectations
Statistics and Probability Letters, 2018The sub-linear expectation space is a nonlinear expectation space having advantages of modeling the uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expectation to replace probability and ...
Li-Xin Zhang, Jinghang Lin
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Skeleton Decomposition and Law of Large Numbers for Supercritical Superprocesses
Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, 2017The goal of this paper is twofold. First, we establish skeleton and spine decompositions for superprocesses whose underlying processes are general symmetric Hunt processes.
Zhen-Qing Chen, Yanxia Ren, Ting Yang
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A Spitzer-type law of large numbers for widely orthant dependent random variables
Statistics and Probability Letters, 2019It is well known that, for a sequence of independent and identically distributed random variables { X , X n , n ≥ 1 } , E X = 0 implies ∑ n = 1 ∞ n − 1 P ( max 1 ≤ k ≤ n | S k | > e n ) ∞ , ∀ e > 0 (Spitzer’s law), where S n = X 1 + ⋯ + X n .
Pingyan Chen, S. Sung
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On a Weak Law of Large Numbers with Regularly Varying Normalizing Sequences
Journal of theoretical probability, 2021F. Boukhari
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