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09 February 2025
 
  » arxiv » 1608.8887

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Exact Berry-Esseen bounds for martingales
Xiequan Fan ;
Date 4 Sep 2016
AbstractRenz (1996), El Machkouri and Ouchti (2007) and Mourrat (2013) have established the bounds on the rate of convergence in the central limit theorem for discrete time martingales. In the present paper a modification of the methods, developed by Bolthausen (1982) and Grama and Haeusler (2000), is applied for obtaining exact rates of convergence in the central limit theorem for martingales with differences having conditional moments of order $2+ ho, ho>0$. Our results significantly improve and generalise the bounds of Renz (1996), El Machkouri and Ouchti (2007) and Mourrat (2013).
Source arXiv, 1608.8887
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