On the Bounds for Convergence Rates in Combinatorial Strong Limit Theorems and Their Applications

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On the Bounds for Convergence Rates in Combinatorial Strong Limit Theorems and Their Applications. / Frolov, A. N. .

в: Vestnik St. Petersburg University: Mathematics, Том 53, № 4, 13.12.2020, стр. 443-449.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{575dfbcb4bcd403c94cf3b51ced4c4a2,

title = "On the Bounds for Convergence Rates in Combinatorial Strong Limit Theorems and Their Applications",

abstract = "The necessary and sufficient conditions are found for convergences of series of weighted probabilities of large deviations for combinatorial sums ∑iXniπn(i), where ||Xnij|| is an n-order matrix of independent random variables and (πn(1), πn(2), …, πn(n)) is a random permutation with the uniform distribution on the set of permutations of numbers 1, 2, …, n independent of Xnij. Combinatorial variants of the results of convergence rates are obtained in the strong law of large numbers and in the law of the iterated logarithm under close to optimal conditions. Applications to rank statistics are discussed.",

keywords = "combinatorial sums, convergence rate, law of the iterated logarithm, strong law of large numbers, Baum–Katz bounds, combinatorial strong law of large numbers, combinatorial law of the iterated logarithm, rank statistics, Spearman{\textquoteright}s coefficient of rank correlation",

author = "Frolov, {A. N.}",

note = "Frolov, A.N. On the Bounds for Convergence Rates in Combinatorial Strong Limit Theorems and Their Applications. Vestnik St.Petersb. Univ.Math. 53, 443–449 (2020). https://doi.org/10.1134/S1063454120040056",

year = "2020",

month = dec,

day = "13",

language = "English",

volume = "53",

pages = "443--449",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - On the Bounds for Convergence Rates in Combinatorial Strong Limit Theorems and Their Applications

AU - Frolov, A. N.

N1 - Frolov, A.N. On the Bounds for Convergence Rates in Combinatorial Strong Limit Theorems and Their Applications. Vestnik St.Petersb. Univ.Math. 53, 443–449 (2020). https://doi.org/10.1134/S1063454120040056

PY - 2020/12/13

Y1 - 2020/12/13

N2 - The necessary and sufficient conditions are found for convergences of series of weighted probabilities of large deviations for combinatorial sums ∑iXniπn(i), where ||Xnij|| is an n-order matrix of independent random variables and (πn(1), πn(2), …, πn(n)) is a random permutation with the uniform distribution on the set of permutations of numbers 1, 2, …, n independent of Xnij. Combinatorial variants of the results of convergence rates are obtained in the strong law of large numbers and in the law of the iterated logarithm under close to optimal conditions. Applications to rank statistics are discussed.

AB - The necessary and sufficient conditions are found for convergences of series of weighted probabilities of large deviations for combinatorial sums ∑iXniπn(i), where ||Xnij|| is an n-order matrix of independent random variables and (πn(1), πn(2), …, πn(n)) is a random permutation with the uniform distribution on the set of permutations of numbers 1, 2, …, n independent of Xnij. Combinatorial variants of the results of convergence rates are obtained in the strong law of large numbers and in the law of the iterated logarithm under close to optimal conditions. Applications to rank statistics are discussed.

KW - combinatorial sums

KW - convergence rate

KW - law of the iterated logarithm

KW - strong law of large numbers

KW - Baum–Katz bounds

KW - combinatorial strong law of large numbers

KW - combinatorial law of the iterated logarithm

KW - rank statistics

KW - Spearman’s coefficient of rank correlation

UR - https://link.springer.com/article/10.1134/S1063454120040056

M3 - Article

VL - 53

SP - 443

EP - 449

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 70767530