Almost sure functional limit theorem for the product of partial sums

Khurelbaatar Gonchigdanzan

ESAIM: Probability and Statistics (2010)

  • Volume: 14, page 338-342
  • ISSN: 1292-8100

Abstract

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We prove an almost sure functional limit theorem for the product of partial sums of i.i.d. positive random variables with finite second moment.

How to cite

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Gonchigdanzan, Khurelbaatar. "Almost sure functional limit theorem for the product of partial sums." ESAIM: Probability and Statistics 14 (2010): 338-342. <http://eudml.org/doc/250817>.

@article{Gonchigdanzan2010,
abstract = { We prove an almost sure functional limit theorem for the product of partial sums of i.i.d. positive random variables with finite second moment. },
author = {Gonchigdanzan, Khurelbaatar},
journal = {ESAIM: Probability and Statistics},
keywords = {Almost sure limit theorem; functional theorem; invariance principle; product of partial sums; almost sure limit theorem},
language = {eng},
month = {10},
pages = {338-342},
publisher = {EDP Sciences},
title = {Almost sure functional limit theorem for the product of partial sums},
url = {http://eudml.org/doc/250817},
volume = {14},
year = {2010},
}

TY - JOUR
AU - Gonchigdanzan, Khurelbaatar
TI - Almost sure functional limit theorem for the product of partial sums
JO - ESAIM: Probability and Statistics
DA - 2010/10//
PB - EDP Sciences
VL - 14
SP - 338
EP - 342
AB - We prove an almost sure functional limit theorem for the product of partial sums of i.i.d. positive random variables with finite second moment.
LA - eng
KW - Almost sure limit theorem; functional theorem; invariance principle; product of partial sums; almost sure limit theorem
UR - http://eudml.org/doc/250817
ER -

References

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  1. B.C. Arnold and J.A. Villaseñor, The asymptotic distribution of sums of records. Extremes1 (1998) 351–363.  Zbl0931.60011
  2. I. Berkes and H. Dehling, Some limit theorems in log density. Ann. Probab.21 (1993) 1640–1670.  Zbl0785.60014
  3. K. Gonchigdanzan and G. Rempała, A note on the almost sure limit theorem for the product of partial sums. Appl. Math. Lett.19 (2006) 191–196.  Zbl1088.60021
  4. G. Rempała and J. Wesołowski, Asymptotics for products of sums and U-statistics. Electron. Commun. Probab.7 (2002) 47–54.  Zbl1008.62048
  5. Y. Qi, Limit distributions for products of sums. Statist. Probab. Lett.62 (2003) 93–100.  Zbl1101.62311
  6. L. Zhang and W. Huang, A note on the invariance principle of the product of sums of random variables. Electron. Commun. Probab.12 (2007) 51–56.  Zbl1130.60027

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