On the bounded laws of iterated logarithm in Banach space

Dianliang Deng

ESAIM: Probability and Statistics (2005)

  • Volume: 9, page 19-37
  • ISSN: 1292-8100

Abstract

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In the present paper, by using the inequality due to Talagrand’s isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.

How to cite

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Deng, Dianliang. "On the bounded laws of iterated logarithm in Banach space." ESAIM: Probability and Statistics 9 (2005): 19-37. <http://eudml.org/doc/245729>.

@article{Deng2005,
abstract = {In the present paper, by using the inequality due to Talagrand’s isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.},
author = {Deng, Dianliang},
journal = {ESAIM: Probability and Statistics},
keywords = {Banach space; bounded law of iterated logarithm; isoperimetric inequality; rademacher series; self-normalizer; Rademacher series},
language = {eng},
pages = {19-37},
publisher = {EDP-Sciences},
title = {On the bounded laws of iterated logarithm in Banach space},
url = {http://eudml.org/doc/245729},
volume = {9},
year = {2005},
}

TY - JOUR
AU - Deng, Dianliang
TI - On the bounded laws of iterated logarithm in Banach space
JO - ESAIM: Probability and Statistics
PY - 2005
PB - EDP-Sciences
VL - 9
SP - 19
EP - 37
AB - In the present paper, by using the inequality due to Talagrand’s isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.
LA - eng
KW - Banach space; bounded law of iterated logarithm; isoperimetric inequality; rademacher series; self-normalizer; Rademacher series
UR - http://eudml.org/doc/245729
ER -

References

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  3. [3] X. Chen, On the law of iterated logarithm for independent Banach space valued random variables. Ann. Probab. 21 (1993) 1991–2011. Zbl0791.60005
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  9. [9] A. Godbole, Self-normalized bounded laws of the iterated logarithm in Banach spaces, in Probability in Banach Spaces 8, R. Dudley, M. Hahn and J. Kuelbs Eds. Birkhäuser Progr. Probab. 30 (1992) 292–303. Zbl0787.60011
  10. [10] P. Griffin and J. Kuelbs, Self-normalized laws of the iterated logarithm. Ann. Probab. 17 (1989) 1571–1601. Zbl0687.60033
  11. [11] P. Griffin and J. Kuelbs, Some extensions of the LIL via self-normalizations. Ann. Probab. 19 (1991) 380–395. Zbl0722.60028
  12. [12] M. Ledoux and M. Talagrand, Characterization of the law of the iterated logarithm in Babach spaces. Ann. Probab. 16 (1988) 1242–1264. Zbl0662.60008
  13. [13] M. Ledoux and M. Talagrand, Some applications of isoperimetric methods to strong limit theorems for sums of independent random variables. Ann. Probab. 18 (1990) 754–789. Zbl0713.60005
  14. [14] M. Ledoux and M. Talagrand, Probability in Banach Space. Springer-Verlag, Berlin (1991). Zbl0748.60004MR1102015
  15. [15] R. Wittmann, A general law of iterated logarithm. Z. Wahrsch. verw. Gebiete 68 (1985) 521–543. Zbl0547.60036

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