Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

STRASSEN'S FUNCTIONAL LIL FOR d-DIMENSIONAL SELF-SIMILAR GAUSSIAN PROCESS IN HOLDER NORM

  • HWANG, KYO-SHIN (Research Institute of Natural Science Goengsang National University) ;
  • LIN, ZHENGYAN (Department of Mathmaitics Zhejiang University)
  • Published : 2005.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, based on large deviation probabilities on Gaussian random vectors, we obtain Strassen's functional LIL for d-dimensional self-similar Gaussian process in Holder norm via estimating large deviation probabilities for d-dimensional self-similar Gaussian process in Holder norm.

Keywords

References

  1. P. Baldi, Large deviations and stochastic homogenization, Ann. Mat. Pura. Appl. (4) 151 (1988), 161-178 https://doi.org/10.1007/BF01762793
  2. P. Baldi, G. Ben Arous, and G. Kerkyacharian, Large deviations and the Strassen theorem in Holder norm, Stochastic Process Appl. 42 (1992), 170-180
  3. P. Baldi and B. Roynette, Some exact equivalent for the Brownian motion in HÄolder norm, Probab. Theory Related Fields 93 (1992), 457-484 https://doi.org/10.1007/BF01192717
  4. B. Chen, Ph. D. Dissertation, Univ. Carleton of Canada (Ottawa, Canada) (1998)
  5. Z. Ciesielek, Some properties of Schauder basis of the space C$_{<0,1>}$, Bull. Polish Acad. Sci. Math. 8 (1960), no. 3, 141-144
  6. Z. Ciesielek, On the isomorphism of the spaces $H_{\alpha}$ and m, Bull. Polish Acad. Sci. Math. 8 (1960), no. 4, 217-222
  7. V. Goodman and J. Kuelbs, Rate of clustering for some Gaussian self-similar processes, Probab. Theory Related Fields 88 (1991), 47-75 https://doi.org/10.1007/BF01193582
  8. L. Gross, Lectures in modern analysis and applications II, Lecture Notes in Math. Springer, Berlin 140 (1970)
  9. J. Kuelbs, The law of the iterated logarithm and related strong convergence theorems for Banach space valued random variables, Lecture Notes in Math. 539 (1976)
  10. J. Kuelbs, A strong convergence theorem for Banach space valued random vari- ables, Ann. Probab. 4 (1976), 744-771 https://doi.org/10.1214/aop/1176995982
  11. J. Kuelbs and W. V. Li, Small ball estimates for Brownian motion and the Brownian sheet, J. Theoret. Probab. 6 (1993), no. 3, 547-577 https://doi.org/10.1007/BF01066717
  12. J. Kuelbs, W. V. Li, and Q. M. Shao, Small ball probabilities for Gaussian processes with stationary increments under Holder norms, J. Theoret. Probab. 8 (1995), no. 2, 361-386 https://doi.org/10.1007/BF02212884
  13. D. Monrad and H. Rootzen, Small values of Gaussian processes and functional laws of the iterated logarithm, Probab. Theory Related Fields 101 (1995), 173- 192 https://doi.org/10.1007/BF01375823
  14. H. Oodaira, On Strassen's version of the law of the iterated for Gaussian processes, Z. Wahrsch. verw. Gebiete 21 (1972), 289-299 https://doi.org/10.1007/BF00532259
  15. J. Ortega, On the size of the increments of non-stationary Gaussian processes, Stochastic Process Appl. 18 (1984), 47-56 https://doi.org/10.1016/0304-4149(84)90160-1
  16. V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrsch. verw. Gebiete 3 (1964), 211-226 https://doi.org/10.1007/BF00534910
  17. W. S. Wang, On a functional limit results for increments of a fractional Brownian motion, Acta Math. Hungar. 93 (2001), no. 1-2, 157-170
  18. W. S. Wang, Functional limit theorems for increments of Gaussian samples, J. Theoret. Probab. 18 (2005), no. 2, 327-343 https://doi.org/10.1007/s10959-005-3505-x
  19. Q. Wei, Functional limit theorems for C-R increments of k-dimensional Brownian motion in Holder norm, Acta Math. Sinica (English series) 16 (2000), no. 4, 637-654 https://doi.org/10.1007/s101140000080

Cited by

  1. Functional Limit Theorems for d–dimensional FBM in Hölder Norm vol.22, pp.6, 2006, https://doi.org/10.1007/s10114-005-0744-9
  2. Functional limit theorems for the increments of d-dimensional Gaussian processes in a Hölder type norm vol.54, pp.5, 2007, https://doi.org/10.1016/j.camwa.2006.12.033