ASYMPTOTIC BEHAVIORS FOR CORRELATED BERNOULLI MODEL
2019 ◽
Vol 34
(4)
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pp. 570-582
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AbstractWe 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.
2001 ◽
Vol 120
(3)
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pp. 499-503
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2019 ◽
Vol 20
(03)
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pp. 2050015
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2000 ◽
Vol 50
(4)
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pp. 357-363
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1955 ◽
Vol 41
(8)
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pp. 586-587
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2016 ◽
Vol 45
(21)
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pp. 6209-6222
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