# Almost sure functional limit theorem for the product of partial sums

ESAIM: Probability and Statistics (2010)

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

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topGonchigdanzan, 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

top- B.C. Arnold and J.A. Villaseñor, The asymptotic distribution of sums of records. Extremes1 (1998) 351–363.
- I. Berkes and H. Dehling, Some limit theorems in log density. Ann. Probab.21 (1993) 1640–1670.
- 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.
- G. Rempała and J. Wesołowski, Asymptotics for products of sums and U-statistics. Electron. Commun. Probab.7 (2002) 47–54.
- Y. Qi, Limit distributions for products of sums. Statist. Probab. Lett.62 (2003) 93–100.
- 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.

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