Gaussian chaos and functional laws of the iterated logarithm for Ito-Wiener integrals

V. Goodman; J. Kuelbs

Annales de l'I.H.P. Probabilités et statistiques (1993)

  • Volume: 29, Issue: 4, page 485-512
  • ISSN: 0246-0203

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Goodman, V., and Kuelbs, J.. "Gaussian chaos and functional laws of the iterated logarithm for Ito-Wiener integrals." Annales de l'I.H.P. Probabilités et statistiques 29.4 (1993): 485-512. <http://eudml.org/doc/77467>.

@article{Goodman1993,
author = {Goodman, V., Kuelbs, J.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stationary Gaussian random variables; rates of convergence; Hausdorff metric; multiple Wiener-Itô integrals},
language = {eng},
number = {4},
pages = {485-512},
publisher = {Gauthier-Villars},
title = {Gaussian chaos and functional laws of the iterated logarithm for Ito-Wiener integrals},
url = {http://eudml.org/doc/77467},
volume = {29},
year = {1993},
}

TY - JOUR
AU - Goodman, V.
AU - Kuelbs, J.
TI - Gaussian chaos and functional laws of the iterated logarithm for Ito-Wiener integrals
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1993
PB - Gauthier-Villars
VL - 29
IS - 4
SP - 485
EP - 512
LA - eng
KW - stationary Gaussian random variables; rates of convergence; Hausdorff metric; multiple Wiener-Itô integrals
UR - http://eudml.org/doc/77467
ER -

References

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  1. [AG] M. Arcones and E. Giné, On Decoupling, Series Expansions, and Tail Behaviour of Chaos Processes, preprint, 1991. MR1201060
  2. [Ba] P. Baldi, Large Deviations and Functional Iterated Logarithm Law for Diffusion Processes, Probab. Th. Rel. Fields, Vol. 71, 1986, pp. 435-453. Zbl0587.60074MR824713
  3. [BO78] C. Borell, Tail Probabilties on Gauss Space, Lecture Notes in Math., Vol. 644, 1978, p. 73-82, Springer, Berlin. Zbl0397.60015MR502400
  4. [CK] R. Carmona and K. Kono, Convergence en loi et lois du logarithme itere pour vecteurs Gaussiens, Z. Wahrscheinlichkeitstheorie und verw. Gebiete, 1976, pp. 241-267. Zbl0321.60023MR494354
  5. [D] H. Dehling, Almost Sure Approximations for U Statistics, preprint, 1989. MR899988
  6. [GK91] V. Goodman and J. Kuelbs, Rates of Clustering for Some Gaussian Self-Similar Processes, Probab. Th. Rel. Fields, Vol. 88, 1991, pp. 47-75. Zbl0695.60040MR1094077
  7. [GK92] V. Goodman and J. Kuelbs, Rates of Clustering for Weakly Convergent Gaussian Vectors and Some Applications, Probab. on Banach Spaces, Vol. 8, 1992, pp. 304-324, Birkhauser. Zbl0787.60012MR1227627
  8. [G92] K. Grill, Exact Rate of Convergence in Strassen's law of the Iterated Logarithm, Journal of Theor. Probab., Vol. 5, 1992, pp. 197-204. Zbl0747.60028MR1144734
  9. [LT] M. Ledoux and M. Talagrand, Probability on Banach Spaces, Springer, Berlin, 1990. Zbl0748.60004
  10. [MO86] T. Mori and H. Oodaira, The Law of the Iterated Logarithm for Self-Similar Processes Represented by Multiple Wiener Integrals, Probab. Th. Rel. Fields, Vol. 71, 1986, pp. 367-391. Zbl0562.60033MR824710
  11. [MO87] T. Mori and H. Oodaira, The Functional Iterated Logarithm Law for Stochastic Processes Represented by Multiple Wiener Integrals, Probab. Th. Rel. Fields, Vol. 72, 1987, pp. 299-310. Zbl0615.60029MR912656
  12. [PK] P.E. Kopp, Martingales and Stochastic Integrals, Cambridge University Press, Cambridge. Zbl0537.60047MR774050
  13. [T92] M. Talagrand, On the Rate of Clustering in Strassen's LIL for Brownian Motion, Probability on Banach Spaces, Vol. 8, 1992, pp. 339-347, Birkhauser. Zbl0787.60040MR1227629

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