Browse > Article
http://dx.doi.org/10.4134/JKMS.2005.42.6.1215

ON THE INCREMENTS OF A d-DIMENSIONAL GAUSSIAN PROCESS  

LIN ZHENGYAN (Department of Mathematics Zhejiang University)
HWANG KYO-SHIN (Department of Mathematics Zhejiang University, Research Institute of Natural Science Geongsang National University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.6, 2005 , pp. 1215-1230 More about this Journal
Abstract
In this paper we establish some results on the increments of a d-dimensional Gaussian process with the usual Euclidean norm. In particular we obtain the law of iterated logarithm and the Book-Shore type theorem for the increments of ad-dimensional Gaussian process, via estimating upper bounds and lower bounds of large deviation probabilities on the suprema of the d-dimensional Gaussian process.
Keywords
Gaussian process; increment; sample path behaviour;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 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
2 J. Ortega, On the size of the increments of non-stationary Gaussian processes, Stochastic Process Appl. 18 (1984), 47-56
3 Q. M. Shao, p-variation of Gaussian processes with stationary increments, Stu dia Sci. Math. Hungar. 31 (1996), 237-247
4 L. X. Zhang, A Note on liminfs for increments of a fractional Bwownian motion, Acta Math. Hungar. 76 (1997), no. 1-2, 145-154   DOI   ScienceOn
5 L. X. Zhang, Some liminf results on increments of fractional Brownian motion, Acta Math. Hungar. 17 (1996), 209-234
6 M. A. Arcones, On the law of the iterated logarithm for Gaussian processes, J. Theoret. Probab. 8 (1995), no. 4, 877-903   DOI
7 S. M. Berman, Limit theorems for the maximum term in stationary sequence, Ann. Math. Statist. 35 (1964), 502-616   DOI   ScienceOn
8 P. Billingsley, Probability and Measure, J. Wiley & Sons, New York, 1986
9 S. A. Book and T. R. Shore, On large intervals in the Csorgo-Revesz theorem on increments of a Wiener process, Z. Wahrsch. verw. Gebiete 46 (1978), 1-11   DOI
10 Y. K. Choi, Erdos-R enyi-type laws applied Gaussian processes, J. Math. Kyoto Univ. 31 (1991), no. 3, 191-217   DOI
11 Y. K. Choi and N. Kono, How big are the increments of a two-parameter Gaussian process?, J. Theoret. Probab. 12 (1999), no. 1, 105-129   DOI   ScienceOn
12 E. Csaki, M. Csorgo, Z. Y. Lin, and P. Revesz, On infinite series of independent Ornstein-Uhlenbeck processes, Stochastic Process Appl. 39 (1991), 25-44   DOI   ScienceOn
13 Z. Y. Lin, K. S. Hwang, S. Lee, and Y. K. Choi, Path properties of a d- dimensional Gaussian process, Statist. Probab. Lett. 68 (2004), 383-393   DOI   ScienceOn
14 F. X. He and B. Chen, Some results on increments of the Wiener process, Chinese J. Appl. Probab. Statist. 5 (1989), 317-326
15 N. Kono, The exact modulus of continuity for Gaussian processes taking values of a finite dimensional normed space in: Trends in Probability and Related Analysis, SAP'96, World Scientific, Singapore, 1996, pp. 219-232
16 Z. Y. Lin, How big the increments of a multifractional Brownian motion?, Sci. China Ser. A 45 (2002), no. 10, 1291-1300
17 Z. Y. Lin and C. R. Lu, Strong Limit Theorems, Science Press, Kluwer Academic Publishers, Hong Kong, 1992
18 Z. Y. Lin and Y. C. Qin, On the increments of $1^{\infty}$-valued Gaussian processes, Asym. Methods in Probab. and Statist.(Ottawa), Elsevier, 1998, 293-302
19 E. Csaki, M. Csorgo, and Q. M. Shao, Fernique type inequalities and moduli of continuity for ${\iota}^2-valued$ Ornstein-Uhlenbeck processes, Ann. Inst. H. Poincare 28 (1992), no. 4, 479-517
20 C. R. Lu, Some results on increments of Gaussian processes, Chinese J. Appl. Probab. Statist. 2 (1986), 59-65
21 M. Csorgo, Z. Y. Lin, and Q. M. Shao, Path properties for $1^{\infty}$ -valued Gaussian processes, Proc. Amer. Math. Soc. 121 (1994), 225-236   DOI   ScienceOn
22 M. Csorgo and P. Revesz, Strong Approximations in Probability and Statistic, Academic Press, New York, 1981
23 M. Csorgo and Q. M. Shao, Strong limit theorems for large and small increments of ${\iota}^p-valued$ Gaussian processes, Ann. Probab. 21 (1993), no. 4, 1958-1990   DOI   ScienceOn
24 X. Fernique, Continuite des processus Gaussiens, C. R. Math. Acad. Sci. Paris 258 (1964), 6058-6060
25 P. Revesz, A generalization of Strassen's funtional law of iterated logarithm, Z. Wahrsch. verw. Gebiete 50 (1979b), 257-264   DOI