Complete and complete moment convergence for i.i.d. random variables under exponential moment conditions |
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| Authors: | Qiu Dehua Chen Pingyan |
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| Institution: | 1. School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, P.R. China;2. Department of Mathematics, Jinan University, Guangzhou, P.R. China |
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| Abstract: | In this paper, we establish a complete convergence result and a complete moment convergence result for i.i.d. random variables under moment condition which is slightly weaker than the existence of the moment generating function. The main results extend and improve the related known results of Lanzinger (1998 Lanzinger, H. (1998). A Baum-Katz theorem for random variables under exponential moment conditions. Stat. Probab. Lett. 39(2):89–95.Crossref], Web of Science ®] , Google Scholar]) and Gut and Stadtmüller (2011 Gut, A., Stadtmüller, U. (2011). An intermediate Baum-Katz theorem. Stat. Probab. Lett. 81(10):1486–1492.Crossref], Web of Science ®] , Google Scholar]). |
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| Keywords: | Complete convergence Complete moment convergence Sums of i i d random variables |
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