A complete characterization of a correlated Bernoulli process
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917636956225536 |
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| author | González-Navarrete, Manuel Lambert, Rodrigo Guevara, Victor Hugo Vázquez |
| author_facet | González-Navarrete, Manuel Lambert, Rodrigo Guevara, Victor Hugo Vázquez |
| contents | We present a complete characterization of the asymptotic behaviour of a correlated Bernoulli sequence { which depends on the parameter $θ\in [0,1]$. A martingale theory based approach will allow} us to prove versions of the law of large numbers, quadratic strong law, law of iterated logarithm, almost sure central limit theorem and functional central limit theorem, in the case $θ\le 1/2$. For $θ> 1/2$, we will obtain a strong convergence to a non-degenerated random variable, including a central limit theorem and a law of iterated logarithm for the fluctuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A complete characterization of a correlated Bernoulli process González-Navarrete, Manuel Lambert, Rodrigo Guevara, Victor Hugo Vázquez Probability We present a complete characterization of the asymptotic behaviour of a correlated Bernoulli sequence { which depends on the parameter $θ\in [0,1]$. A martingale theory based approach will allow} us to prove versions of the law of large numbers, quadratic strong law, law of iterated logarithm, almost sure central limit theorem and functional central limit theorem, in the case $θ\le 1/2$. For $θ> 1/2$, we will obtain a strong convergence to a non-degenerated random variable, including a central limit theorem and a law of iterated logarithm for the fluctuations. |
| title | A complete characterization of a correlated Bernoulli process |
| topic | Probability |
| url | https://arxiv.org/abs/2404.07370 |