Strong laws for sequences in the vicinity of the LIL

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• 作者：Allan Gut^a ; ^{allan.gut@math.uu.se} ; ; Ulrich Stadtmü ; ller^b ; ^{ulrich.stadtmueller@uni-ulm.de} ;
• 关键词：primary ; 60F15 ; 60G50 ; 60G60 ; secondary ; 60F05
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：122
• 期：Complete
• 页码：63-72
• 全文大小：432 K
• 卷排序：122

文摘

The present paper is devoted to strong laws of large numbers under moment conditions near those of the law of the iterated logarithm (LIL) for i.i.d sequences. More precisely, we wish to investigate possible limit theorems under moment conditions which are stronger than pp for any p<2p<2, in which case we know that there is a.s. convergence to 0, and weaker than EX2<∞, in which case the LIL holds.