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On the rates of convergence in weak limit theorems for geometric random sums of the strictly stationary sequence of m-dependent random variables

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Abstract

In this paper, we consider a strictly stationary sequence of m-dependent random variables through a compatible sequence of independent and identically distributed random variables by the moving averages processes. Using the Zolotarev distance, we estimate some rates of convergence in the weak limit theorems for normalized geometric random sums of the strictly stationary sequence of m-dependent random variables. The obtained results are extensions and generalizations of several known results on geometric random sums of independent and identically distributed random variables.

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  • 06 June 2020

    In the metadata of the article on SpringerLink, the corresponding author is incorrect. The corresponding author is Tran Loc Hung (tlhung@ufm.edu.vn; tlhungvn@gmail.com)

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Authors and Affiliations

  1. University of Finance and Marketing, 2/4 Tran Xuan Soan Street, District No. 7, Ho Chi Minh City, Vietnam

    Tran Loc Hung & Phan TriKien

  2. University of Science – VNU. HCMC, 227 Nguyen Van Cu Street, District No. 5, Ho Chi Minh City, Vietnam

    Phan TriKien

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  1. Tran Loc Hung
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  2. Phan TriKien
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Correspondence to Phan TriKien.

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The first author was supported in part by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant 101.01-2010.02.

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Hung, T.L., TriKien, P. On the rates of convergence in weak limit theorems for geometric random sums of the strictly stationary sequence of m-dependent random variables. Lith Math J 60, 173–188 (2020). https://doi.org/10.1007/s10986-020-09478-6

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  • DOI: https://doi.org/10.1007/s10986-020-09478-6

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