The limit theorems for a previous k-sum dependent model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Singh, Deepak¹  Kumar, Somesh¹  Vellaisamy, P.² 

[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India

[2] Indian Inst Technol, Dept Math, Powai Mumbai 400076, India

关键词: Dependent Bernoulli random variables;    Generalized binomial distribution;    Martingale;    Central limit theorem;    Law of large numbers;    Short and long range dependence;   

DOI  :  10.1016/j.jmaa.2020.124004

来源: Elsevier

【 摘 要 】

The main goal of this paper is to establish limit theorems for the sums of dependent Bernoulli random variables. Here each successive random variable depends on previous few random variables. A previous k-sum dependent model is considered. This model is a combination of the previous all sum and the previous k-sum dependent models. The strong law of large numbers, the central limit theorem and the law of iterated logarithm for the sums of random variables following this model are established. A new approach using martingale differences is developed to prove these results. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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