JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CHUNG-TYPE LAW OF THE ITERATED LOGARITHM OF l-VALUED GAUSSIAN PROCESSES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
CHUNG-TYPE LAW OF THE ITERATED LOGARITHM OF l-VALUED GAUSSIAN PROCESSES
Choi, Yong-Kab; Lin, Zhenyan; Wang, Wensheng;
  PDF(new window)
 Abstract
In this paper, by estimating small ball probabilities of -valued Gaussian processes, we investigate Chung-type law of the iterated logarithm of -valued Gaussian processes. As an application, the Chung-type law of the iterated logarithm of -valued fractional Brownian motion is established.
 Keywords
small ball probability;Gaussian process;law of the iterated logarithm;
 Language
English
 Cited by
 References
1.
E. Csáki and M. Csörgő, Inequalities for increments of stochastic processes and moduli of continuity, Ann. Probab. 20 (1992), no. 2, 1031–1052. crossref(new window)

2.
M. Csörgő, Z. Lin, and Q.-M. Shao, Path properties for $l^{\infty}$-valued Gaussian processes, Proc. Amer. Math. Soc. 121 (1994), no. 1, 225–236. crossref(new window)

3.
M. Csörgő and P. Révész, Strong Approximations in Probability and Statistics, New York, Academic Press, 1981.

4.
M. Csörgő and Q.-M. Shao, Strong limit theorems for large and small increments of $l^p$-valued Gaussian processes, Ann. Probab. 21 (1993), no. 4, 1958–1990. crossref(new window)

5.
J. Hoffmann-Jørgensen, L. A. Shepp, and R. M. Dudley, On the lower tail of Gaussian seminorms, Ann. Probab. 7 (1979), no. 2, 319–342. crossref(new window)

6.
J.-P. Kahane, Some Random Series of Functions, 2nd edition, Cambridge Studies in Advanced Mathematics, 5. Cambridge University Press, Cambridge, 1985.

7.
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. crossref(new window)

8.
M. Ledoux and M. Talagrand, Probability in Banach Space, New York, Springer-Verlag, 1991.

9.
Z. Lin and Y. Qin, On large increments of $l^{\infty}$-valued Gaussian processes, In: Asym. Methods in Probab. and Statist., The Proceeding Volume of ICAMPS'97 (B. Szyszkowicz, Ed). Elsevier Scence B. V., Amsterdam, 1998.

10.
Z. Lin, C. Lu, and L.-X. Zhang, Path Properties of Gaussian Processes, Zhejiang Univ. Press, 2001.

11.
D. Monrad and H. Rootz´en, Small values of Gaussian processes and functional laws of the iterated logarithm, Probab. Theory Related Fields 101 (1995), no. 2, 173–192. crossref(new window)

12.
G. Samorodnitsky and M. S. Taqqu, Stable non-Gaussian Random Processes: Stochastic Models with infinite variance, Chapman & Hall, New York, 1994.

13.
Q.-M. Shao and D. Wang, Small ball probabilities of Gaussian fields, Probab. Theory Related Fields 102 (1995), no. 4, 511–517. crossref(new window)

14.
W. Wang and L.-X. Zhang, Chung-type law of the iterated logarithm on lp-valued Gaussian processes, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 2, 551–560. crossref(new window)