On the local limit theorems for linear sequences of lower psi-mixing Markov chains

被引：0

作者：

Peligrad, Magda ^{[1
]}

Sang, Hailin ^{[2
]}

Zhang, Na ^{[3
]}

机构：

[1] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

[2] Univ Mississippi, Dept Math, University, MS 38677 USA

[3] Towson Univ, Dept Math, Towson, MD 21252 USA

来源：

STATISTICS & PROBABILITY LETTERS | 2024年 / 210卷

基金：

美国国家科学基金会;

关键词：

Local limit theorem; Markov chains; Psi-mixing; SUMS;

D O I：

10.1016/j.spl.2024.110108

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we investigate the local limit theorem for partial sums of linear sequences of the form X (j) = Sigma(i is an element of Z) a (i) e (j - i) . Here (a(i)) (i is an element of Z) is a sequence of constants satisfying Sigma(i is an element of Z) a(i)(2) < infinity and (xi(i))(i is an element of Z) are functions of a stationary Markov chain with mean zero and finite second moment. The Markov chain is assumed to satisfy one-sided lower psi -mixing condition.

引用

页数：11

共 22 条

[1] Billingsley Patrick, 1995, Probability and Measure, Vthird
[2] Bradley R.C., 2007, Introduction To Strong Mixing Conditions
[3] Every "lower psi-mixing" Markov chain is "interlaced rho-mixing"
Bradley, RC
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1997, 72 (02) : 221 - 239
[4] Breiman L., 1992, Probability, DOI DOI 10.1137/1.9781611971286
[5] Invariance principles for linear processes with application to isotonic regression
Dedecker, Jerome
Merlevede, Florence
Peligrad, Magda
[J]. BERNOULLI, 2011, 17 (01) : 88 - 113
[6] A Local Limit Theorem for sums of independent random vectors
Dolgopyat, Dmitry
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2016, 21
[7] A local limit theorem for linear random fields
Fortune, Timothy
Peligrad, Magda
Sang, Hailin
[J]. JOURNAL OF TIME SERIES ANALYSIS, 2021, 42 (5-6) : 696 - 710
[8] Gnedenko B.V., 1962, THEORY PROBABILITY
[9] A Nonconventional Local Limit Theorem
Hafouta, Yeor
Kifer, Yuri
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2016, 29 (04) : 1524 - 1553
[10] Ibragimov I. A., 1971, INDEPENDENT STATIONA

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