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ASYMPTOTIC BEHAVIORS FOR CORRELATED BERNOULLI MODEL
- Part of
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- Journal:
- Probability in the Engineering and Informational Sciences / Volume 34 / Issue 4 / October 2020
- Published online by Cambridge University Press:
- 11 July 2019, pp. 570-582
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- Article
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We consider a class of correlated Bernoulli variables, which have the following form: for some 0 < p < 1,
where 0 ≤ θj ≤ 1,
$$\begin{align}{P(X_{j+1}=1 \vert {\cal F}_{j})= (1-\theta_j)p+\theta_jS_j/j,}\end{align}$$
$S_n=\sum _{j=1}^nX_j$ 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.
