Some exact rates in the functional law of the iterated logarithm

Philippe Berthet; Mikhail Lifshits

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 6, page 811-824
  • ISSN: 0246-0203

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Berthet, Philippe, and Lifshits, Mikhail. "Some exact rates in the functional law of the iterated logarithm." Annales de l'I.H.P. Probabilités et statistiques 38.6 (2002): 811-824. <http://eudml.org/doc/77742>.

@article{Berthet2002,
author = {Berthet, Philippe, Lifshits, Mikhail},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {exact convergence rate; functional laws; Chung's law; Brownian motion; Wiener process; small ball probabilities},
language = {eng},
number = {6},
pages = {811-824},
publisher = {Elsevier},
title = {Some exact rates in the functional law of the iterated logarithm},
url = {http://eudml.org/doc/77742},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Berthet, Philippe
AU - Lifshits, Mikhail
TI - Some exact rates in the functional law of the iterated logarithm
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 6
SP - 811
EP - 824
LA - eng
KW - exact convergence rate; functional laws; Chung's law; Brownian motion; Wiener process; small ball probabilities
UR - http://eudml.org/doc/77742
ER -

References

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  1. [1] P. Berthet, Z. Shi, Small ball estimates for Brownian motion under a weighted sup-norm, Studia Sci. Math. Hungarica36 (2000) 275-289. Zbl0973.60083MR1768227
  2. [2] K.L. Chung, On the maximum partial sums of sequences of independent random variables, Trans. Amer. Math. Soc.64 (1948) 205-233. Zbl0032.17102MR26274
  3. [3] E. Csáki, A relation between Chung's and Strassen's law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie Verw. Gebeite54 (1980) 287-301. Zbl0441.60027MR602512
  4. [4] E. Csáki, A liminf result in Strassen's law of the iterated logarithm, Colloq. Math. Soc. János Bolyai57 (1989) 83-93. Zbl0719.60033MR1116781
  5. [5] J.D. Deuschel, D.M. Stroock, Large Deviations, Academic Press, 1989. Zbl0705.60029MR997938
  6. [6] A. De Acosta, Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm, Ann. Probab.11 (1983) 78-101. Zbl0504.60033MR682802
  7. [7] V. Goodman, J. Kuelbs, Rates of clustering in Strassen's LIL for Brownian motion, J. Theoret. Probab.4 (1991) 285-309. Zbl0724.60034MR1100235
  8. [8] N. Gorn, M. Lifshits, Chung's law and the Csáki function, J. Theoret. Probab.12 (1999) 399-420. Zbl0937.60013MR1684751
  9. [9] K. Grill, A liminf result in Strassen's law of the iterated logarithm, Probab. Theory Related Fields89 (1991) 149-157. Zbl0722.60030MR1110535
  10. [10] J. Kuelbs, W.V. Li, M. Talagrand, Liminf results for Gaussian samples and Chung's functional LIL, Ann. Probab.22 (1994) 1879-1903. Zbl0849.60022MR1331209
  11. [11] A.A. Mogulskii, Small deviations in a space of trajectories, Theoret. Probab. Appl.19 (1974) 726-736. Zbl0326.60061MR370701
  12. [12] V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie Verw. Gebeite3 (1964) 211-226. Zbl0132.12903MR175194

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