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An Extension of Almost Sure Central Limit Theory for the Product of Partial Sums
Miao Yuyumiao728@yahoo.com.cnCollege of Mathematics and Information ScienceHenan Normal UniversityHenan, 453007, ChinaView full profile →
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- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2009.10698562
- Pages:
- 49–60
Abstract
An almost sure central limit theorem for the product of the partial sums of i.i.d. positive random variables is shown, which is an extension of Gonchigdanzan and Rempała [5]. Moreover, a more general almost sure central limit theorem for a triangular array is proved.
Keywords
References
- Arnold, B.C. and Villaseñor, J.A.1998 . The asymptotic distribution of sums of records . , 1 ( 3 ) : 351 – 363 .
- Berkes, I. and Csáki, E.2001 . A universal result in almost sure central limit theory . , 94 : 105 – 134 .
- Berkes, I. and Horváth, L.2001 . The logarithmic average of sample extremes is asymptotically normal . , 91 ( 1 ) : 77 – 98 .
- Csáki, E. and Gonchigdanzan, K.2002 . Almost sure limit theorems for the maximum of stationary Gaussian sequences . , 58 ( 2 ) : 195 – 203 .
- Gonchigdanzan, K. and Rempała, G. A.2006 . A note on the almost sure limit theorem for the product of partial sums . , 19 : 191 – 196 .
- Hörmann, S.2006 . An extension of almost sure central limit theory . , 76 : 191 – 202 .
- Lacey, M.T. and Philipp, W.1990 . A note on the almost sure central limit theorem . , 9 : 201 – 205 .
- Miao, Y.2008 . Central limit theorem and almost sure central limit theorem for the product of some partial sums . , 118 ( 2 ) : 289 – 294 .
- Rempała, G.A. and Wesołowski, J.2002 . Asymptotics for products of sums and -statistics . , 7 : 47 – 54 .
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