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On the Strong Law of Large Numbers [PDF]
Proceedings of the American Mathematical Society, 1970 indicator variables given by F*(X) = 1 if | Sk — kp\ =\k, and 0 otherwise, and let JV»(X) = z2? ^(X)- Then ATM(X) = Jji" Yk(\) is precisely the "finitely many" random variable of the Strong Law of Large Numbers. Indeed, this law may be formulated in terms of this counting variable as in the following. Strong law of large numbers.
Slivka, J., Severo, N. C.
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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, Daniel Rudolf
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On Combinatorial Strong Law of Large Numbers and Rank Statistics
Vestnik of Saint Petersburg University Mathematics Mechanics Astronomy, 2020 The author had earlier obtained a strong law of large numbers P for combinatorial sums i Xniπn(i) , where kXnijk is a matrix of order n from random variables with finite fourth moments and (πn(1), πn(2), . . . , πn(n)) is a random permutation having
Andrei N. Frolov
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On the Strong Law of Large Numbers [PDF]
Transactions of the American Mathematical Society, 1949 \(f(x) = f(x+1)\) besitze in \((0,1)\) den Mittelwert Null sowie die Streuung Eins und \((n_k)\) sei eine Folge von natürlichen Zahlen mit \(n_{k+1}/n_k > c > 1\). Die Frage, welche Bedingung das sog. starke Gesetz \[ g = \lim_{N\to \infty} \sum_{k=1}^N f(n_k x)/N = 0 \] für fast alle \(x\) sichert, ist von Kac, Salem, Zygmund unlängst mit den \(n ...
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A strong law of large numbers for positive random variables [PDF]
Illinois Journal of Mathematics, 2021 In the spirit of the famous KOML\'OS (1967) theorem, every sequence of nonnegative, measurable functions $\{ f_n \}_{n \in \N}$ on a probability space, contains a subsequence which - along with all its subsequences - converges a.e.
I. Karatzas, W. Schachermayer
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An extension of Feller’s strong law of large numbers [PDF]
Statistics & Probability Letters, 2018 10 pages. arXiv admin note: text overlap with arXiv:1703.07868.
Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada ( host institution ) +3 more
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A Strong Law of Large Numbers for Random Compact Sets
Annals of Probability, 1975 Zvi Artstein, Richard A Vitale
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A Strong Law of Large Numbers for Super-stable Processes. [PDF]
, 2014 Let ℓ be Lebesgue measure and X=(Xt,t≥0;Pμ) be a supercritical, super-stable process corresponding to the operator −(−Δ)α/2u+βu−ηu2 on Rd with constants β,η>0 and α∈(0,2]. Put View the MathML source, which for each smallθ is an a.s. convergent complex-
Kouritzin, Michael, Ren, Y.-X.
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International Journal of Mathematics and Mathematical Sciences, 1999 Let {Xij} be a double sequence of pairwise independent random variables.
Dug Hun Hong, Seok Yoon Hwang
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Further Spitzer’s law for widely orthant dependent random variables
Journal of Inequalities and Applications, 2021 The Spitzer’s law is obtained for the maximum partial sums of widely orthant dependent random variables under more optimal moment conditions.
Pingyan Chen, Jingjing Luo, Soo Hak Sung
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