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ASYMPTOTIC BEHAVIORS FOR CORRELATED BERNOULLI MODEL

Published online by Cambridge University Press:  11 July 2019

Yu Miao
Affiliation:
College of Mathematics and Information Science, Henan Normal University, Henan Province453007, China E-mail: [email protected]; [email protected]
Huanhuan Ma
Affiliation:
College of Mathematics and Information Science, Henan Normal University, Henan Province453007, China E-mail: [email protected]; [email protected]
Qinglong Yang
Affiliation:
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Hubei Province430073, China E-mail: [email protected]

Abstract

We consider a class of correlated Bernoulli variables, which have the following form: for some 0 < p < 1,

$$\begin{align}{P(X_{j+1}=1 \vert {\cal F}_{j})= (1-\theta_j)p+\theta_jS_j/j,}\end{align}$$
where 0 ≤ θj ≤ 1, $S_n=\sum _{j=1}^nX_j$ and ${\cal F}_n=\sigma \{X_1,\ldots , X_n\}$. The aim of this paper is to establish the strong law of large numbers which extend some known results, and prove the moderate deviation principle for the correlated Bernoulli model.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2019

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