Limit behaviors for dependent Bernoulli variables

2020 ◽  
Vol 35 (4) ◽  
pp. 399-409
Author(s):  
Yu Miao ◽  
Huan-huan Ma
Keyword(s):  
Bernoulli Variables

ASYMPTOTIC BEHAVIORS FOR CORRELATED BERNOULLI MODEL

2019 ◽  
Vol 34 (4) ◽  
pp. 570-582
Author(s):  
Yu Miao ◽  
Huanhuan Ma ◽  
Qinglong Yang
Keyword(s):  
Law Of Large Numbers ◽  
Moderate Deviation ◽  
Bernoulli Model ◽  
Strong Law ◽  
Asymptotic Behaviors ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Large Numbers ◽  
Bernoulli Variables ◽  
Image Position

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.

On Sums of Products of Bernoulli Variables and Random Permutations

2004 ◽  
Vol 17 (1) ◽  
pp. 285-292 ◽  
Author(s):  
Anatole Joffe ◽  
Éric Marchand ◽  
François Perron ◽  
Paul Popadiuk
Keyword(s):  
Random Permutations ◽  
Bernoulli Variables ◽  
Sums Of Products

Uniformly distributed sums of bernoulli variables

1988 ◽  
Vol 28 (3) ◽  
pp. 671-677 ◽  
Author(s):  
Hanne Dalgas Christiansen
Keyword(s):  
Bernoulli Variables

scholarly journals Generalized Bernoulli process with long-range dependence and fractional binomial distribution

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Jeonghwa Lee
Keyword(s):  
Long Range ◽  
Infinite Sequence ◽  
Binary Sequence ◽  
Random Variable ◽  
Long Range Dependence ◽  
Bernoulli Process ◽  
Binomial Random Variable ◽  
Fixed Constant ◽  
Bernoulli Variables ◽  
Auto Covariance

Abstract Bernoulli process is a finite or infinite sequence of independent binary variables, X i , i = 1, 2, · · ·, whose outcome is either 1 or 0 with probability P(X i = 1) = p, P(X i = 0) = 1 – p, for a fixed constant p ∈ (0, 1). We will relax the independence condition of Bernoulli variables, and develop a generalized Bernoulli process that is stationary and has auto-covariance function that obeys power law with exponent 2H – 2, H ∈ (0, 1). Generalized Bernoulli process encompasses various forms of binary sequence from an independent binary sequence to a binary sequence that has long-range dependence. Fractional binomial random variable is defined as the sum of n consecutive variables in a generalized Bernoulli process, of particular interest is when its variance is proportional to n 2 H , if H ∈ (1/2, 1).

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