A complete characterization of a correlated Bernoulli process

2024/04/10 by Manuel González-Navarrete, González-Navarrete, Manuel, Rodrigo Lambert +3 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2404.07370

openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a complete characterization of the asymptotic behaviour of a correlated Bernoulli sequence which depends on the parameter θ∈ [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≤ 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.

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