Uniform Central Limit Theorem for martingales

2014/11/08 by L. Sirota, Sirota, L.
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Fuzzy Systems and Optimization #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories #math.PR

paper · pdf · doi:10.48550/arxiv.1411.2171

arxiv created 2014/11/08 · openalex publication_date 2014/11/08 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study some sufficient conditions imposed on the sequence of martingale differences (m.d.) in the separable Banach spaces of continuous functions defined on the metric compact set for the Central Limit Theorem in this space. We taking into account the classical entropy terms, and use the theory of the so-called Grand Lebesgue Spaces of random variables having power and exponential decreasing tail of distribution.

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