One more on the convergence rates in precise asymptotics

In this paper, we establish one general result on precise asymptotics of weighted sums for i.i.d. random variables. As a corollary, we have the results of Lanzinger and Stadtmüller [Refined Baum–Katz laws for weighted sums of iid random variables, Statist. Probab. Lett. 69 (2004) 357–368], Gut and Spătaru [Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000) 1870–1883; Precise asymptotics in the Baum–Katz and Davis laws of large numbers, J. Math. Anal. Appl. 248 (2000) 233–246], Gut and Steinebach [Convergence rates and precise asymptotics for renewal counting processes and some first passage times, Fields Inst. Comm. 44 (2004) 205–227] and Heyde [A supplement to the strong law of large numbers, J. Appl. Probab. 12 (1975) 173–175]. Meanwhile, we provide an answer for the possible conclusion pointed out by Lanzinger and Stadtmüller [Refined Baum–Katz laws for weighted sums of iid random variables, Statist. Probab. Lett. 69 (2004) 357–368].

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A note to the convergence rates in precise asymptotics

Journal of Inequalities and Applications ◽

10.1186/1029-242x-2013-378 ◽

2013 ◽

Vol 2013 (1) ◽

Author(s):

Jianjun He

Keyword(s):

Convergence Rates ◽

Precise Asymptotics

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Convergence rates in the complete moment of moving-average processes

Mathematica Slovaca ◽

10.2478/s12175-012-0058-1 ◽

2012 ◽

Vol 62 (5) ◽

Author(s):

Qing-pei Zang

Keyword(s):

Convergence Rates ◽

Infinite Sequence ◽

Moving Average ◽

Precise Asymptotics ◽

Moving Average Process ◽

Real Numbers ◽

Moment Convergence ◽

Summable Sequence ◽

Moving Average Processes ◽

Independent Identically Distributed

AbstractIn this paper, we discuss precise asymptotics for a new kind of moment convergence of the moving-average process $$X_k = \sum\limits_{i = - \infty }^\infty {a_{i + k} \varepsilon _i }$$, k ≥1, where {ε i: −∞ < i < ∞} is a doubly infinite sequence of independent identically distributed random variables with mean zero and the finiteness of variance, {α i: −∞ < i < ∞} is an absolutely summable sequence of real numbers, i.e., $$\sum\limits_{i = - \infty }^\infty {\left| {a_i } \right| < \infty }$$.

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A note on the convergence rates in precise asymptotics

Journal of Inequalities and Applications ◽

10.1186/s13660-019-1972-3 ◽

2019 ◽

Vol 2019 (1) ◽

Author(s):

Yong Zhang

Keyword(s):

Convergence Rates ◽

Precise Asymptotics

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Second-Order Moment Convergence Rates for Spectral Statistics of Random Matrices

Abstract and Applied Analysis ◽

10.1155/2013/595912 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7

Author(s):

Junshan Xie

Keyword(s):

Random Matrices ◽

Complete Convergence ◽

Convergence Rates ◽

Covariance Matrices ◽

Second Order ◽

Order Moment ◽

Precise Asymptotics ◽

Moment Convergence ◽

Sample Covariance ◽

Spectral Statistics

This paper considers the precise asymptotics of the spectral statistics of random matrices. Following the ideas of Gut and Spătaru (2000) and Liu and Lin (2006) on the precise asymptotics of i.i.d. random variables in the context of the complete convergence and the second-order moment convergence, respectively, we will establish the precise second-order moment convergence rates of a type of series constructed by the spectral statistics of Wigner matrices or sample covariance matrices.

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Convergence rates in precise asymptotics for a kind of complete moment convergence

Stochastics and Dynamics ◽

10.1142/s0219493717500150 ◽

2017 ◽

Vol 17 (02) ◽

pp. 1750015

Author(s):

Lingtao Kong ◽

Hongshuai Dai

Keyword(s):

Complete Convergence ◽

Convergence Rates ◽

Complete Moment Convergence ◽

Precise Asymptotics ◽

Moment Convergence ◽

Special Case

Liu and Lin (Statist. Probab. Lett. 2006) introduced a kind of complete moment convergence which includes complete convergence as a special case. In this paper, we study the convergence rates of the precise asymptotics for complete moment convergence introduced by Liu and Lin (2006) and get the corresponding convergence rates.

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