Browse > Article
http://dx.doi.org/10.4134/JKMS.2005.42.5.959

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)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.5, 2005 , pp. 959-973 More about this Journal
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
d-dimensional Gaussian process; Holder norm; large de­viation probability; self-similar; Strassen's functional law of iterated logarithm;
Citations & Related Records

Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
연도 인용수 순위
1 V. Goodman and J. Kuelbs, Rate of clustering for some Gaussian self-similar processes, Probab. Theory Related Fields 88 (1991), 47-75   DOI
2 L. Gross, Lectures in modern analysis and applications II, Lecture Notes in Math. Springer, Berlin 140 (1970)
3 P. Baldi and B. Roynette, Some exact equivalent for the Brownian motion in HÄolder norm, Probab. Theory Related Fields 93 (1992), 457-484   DOI
4 P. Baldi, Large deviations and stochastic homogenization, Ann. Mat. Pura. Appl. (4) 151 (1988), 161-178   DOI
5 P. Baldi, G. Ben Arous, and G. Kerkyacharian, Large deviations and the Strassen theorem in Holder norm, Stochastic Process Appl. 42 (1992), 170-180
6 B. Chen, Ph. D. Dissertation, Univ. Carleton of Canada (Ottawa, Canada) (1998)
7 Z. Ciesielek, Some properties of Schauder basis of the space C$_{<0,1>}$, Bull. Polish Acad. Sci. Math. 8 (1960), no. 3, 141-144
8 Z. Ciesielek, On the isomorphism of the spaces $H_{\alpha}$ and m, Bull. Polish Acad. Sci. Math. 8 (1960), no. 4, 217-222
9 J. Kuelbs, A strong convergence theorem for Banach space valued random vari- ables, Ann. Probab. 4 (1976), 744-771   DOI   ScienceOn
10 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)
11 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   DOI
12 H. Oodaira, On Strassen's version of the law of the iterated for Gaussian processes, Z. Wahrsch. verw. Gebiete 21 (1972), 289-299   DOI
13 J. Ortega, On the size of the increments of non-stationary Gaussian processes, Stochastic Process Appl. 18 (1984), 47-56   DOI   ScienceOn
14 V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrsch. verw. Gebiete 3 (1964), 211-226   DOI
15 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
16 W. S. Wang, Functional limit theorems for increments of Gaussian samples, J. Theoret. Probab. 18 (2005), no. 2, 327-343   DOI   ScienceOn
17 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   DOI   ScienceOn
18 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   DOI   ScienceOn
19 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   DOI