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Complete moment convergence for i.i.d. random variables
Institution:1. School of Mathematics and Statistics, Guangdong University of Finance & Economics, Guangzhou 510320, PR China;2. Department of Mathematics, Jinan University, Guangzhou 510630, PR China;1. Université de Rouen, LITIS EA 4108, Avenue de l’Université, BP 12, 76801 Saint-Étienne-du-Rouvray, France;2. Rutgers University, Department of Statistics, 561 Hill Center, Busch Campus, Piscataway, NJ 08854-8019, USA;1. Clausthal University of Technology, Department of Applied Stochastics and Operations Research, 38678 Clausthal-Zellerfeld, Germany;2. University of Derby, School of Computing and Mathematics, Derby, DE22 1GB, UK
Abstract:In the paper, the complete moment convergence is obtained for i.i.d. random variables such that all moments exist, but the moment generating function does not exist. The main results extend the related known works due to Gut and Stadtmüller.
Keywords:Sums of i  i  d  random variables  Complete convergence  Complete moment convergence
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