On bounds for convergence rates in combinatorial strong limit theorems and its applications | Zendy

А. Н. Фролов | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

On bounds for convergence rates in combinatorial strong limit theorems and its applications

Author(s) -

А. Н. Фролов

Publication year - 2020

Publication title -

vestnik of saint petersburg university mathematics mechanics astronomy

Language(s) - English

Resource type - Journals

eISSN - 2587-5884

pISSN - 1025-3106

DOI - 10.21638/spbu01.2020.410

Subject(s) - mathematics , law of the iterated logarithm , combinatorics , permutation (music) , random permutation , logarithm , rank (graph theory) , limit (mathematics) , law of large numbers , rate of convergence , central limit theorem , iterated function , distribution (mathematics) , random variable , iterated logarithm , order (exchange) , convergence of random variables , convergence (economics) , matrix (chemical analysis) , discrete mathematics , statistics , symmetric group , mathematical analysis , computer science , channel (broadcasting) , physics , materials science , finance , acoustics , economics , composite material , economic growth , computer network

We find necessary and sufficient conditions for convergences of series of weighted probabilities of large deviations for combinatorial sums i Xniπn(i), where Xnij is a matrix of order n 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 with Xnij. We obtain combinatorial variants of results on convergence rates in the strong law of large numbers and the law of the iterated logarithm under conditions closed to optimal ones. We discuss applications to rank statistics.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research