Gaussian chaos and functional laws of the iterated logarithm for Ito-Wiener integrals
Goodman, V. ; Kuelbs, J.
Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993), p. 485-512 / Harvested from Numdam
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Publié le : 1993-01-01
@article{AIHPB_1993__29_4_485_0,
     author = {Goodman, V. and Kuelbs, James D.},
     title = {Gaussian chaos and functional laws of the iterated logarithm for Ito-Wiener integrals},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {29},
     year = {1993},
     pages = {485-512},
     mrnumber = {1251138},
     zbl = {0805.60027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1993__29_4_485_0}
}

Goodman, V.; Kuelbs, J. Gaussian chaos and functional laws of the iterated logarithm for Ito-Wiener integrals. Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) pp. 485-512. http://gdmltest.u-ga.fr/item/AIHPB_1993__29_4_485_0/

[AG] M. Arcones and E. Giné, On Decoupling, Series Expansions, and Tail Behaviour of Chaos Processes, preprint, 1991. | MR 1201060

[Ba] P. Baldi, Large Deviations and Functional Iterated Logarithm Law for Diffusion Processes, Probab. Th. Rel. Fields, Vol. 71, 1986, pp. 435-453. | MR 824713 | Zbl 0587.60074

[BO78] C. Borell, Tail Probabilties on Gauss Space, Lecture Notes in Math., Vol. 644, 1978, p. 73-82, Springer, Berlin. | MR 502400 | Zbl 0397.60015

[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. | MR 494354 | Zbl 0321.60023

[D] H. Dehling, Almost Sure Approximations for U Statistics, preprint, 1989. | MR 899988

[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. | MR 1094077 | Zbl 0695.60040

[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. | MR 1227627 | Zbl 0787.60012

[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. | MR 1144734 | Zbl 0747.60028

[LT] M. Ledoux and M. Talagrand, Probability on Banach Spaces, Springer, Berlin, 1990. | Zbl 0748.60004

[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. | MR 824710 | Zbl 0562.60033

[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. | MR 912656 | Zbl 0615.60029

[PK] P.E. Kopp, Martingales and Stochastic Integrals, Cambridge University Press, Cambridge. | MR 774050 | Zbl 0537.60047

[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. | MR 1227629 | Zbl 0787.60040