Existence of small ball constants for fractional Brownian motions;L'existence de la limite pour l'asymptotique des petites boules du mouvement brownien fractionnaire

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 326, Issue 11, 1998, Pages 1329-1334

  Li, Wenbo V ^a   Linde, Werner ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032092875     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0764-4442(98)80189-4     Document Type: Article

References (9)

1. [1] Kuelbs J., Li W.V., Small ball estimates for Brownian motion and the Brownian sheet, J. Th. Probab. 6 (1993) 547-577.
2. [2] Ledoux M., Isoperimetry and Gaussian Analysis, Lectures on Probability Theory and Statistics, Lect. Notes in Math. 1648, Springer-Verlag, 1996, pp. 165-294.
3. [3] Li W.V., Linde W., Approximation, metric entropy and small ball estimates for Gaussian measures, Preprint, 1998.
4. [4] Li W.V., Shao Q.M., A note on the Gaussian correlation conjecture and the existence of small ball constant for fractional Brownian motions, Preprint, 1997.
5. [5] Mandelbrot B.B., Van Ness J. W., Fractional Brownian motions, fractional noises, and applications, SIAM Rev. 10 (1968) 422-437.
6. [6] Monrad D., Rootzén H., Small values of Gaussian processes and functional laws of the iterated logarithm, Probab. Th. Rel. Fields 101 (1995) 173-192.
7. [7] Shao Q.M., A note on small ball probability of Gaussian processes with stationary increments, J. Th. Probab. 6 (1993) 595-602.
8. [8] Talagrand M., New Gaussian estimates for enlarged balls, Geom. Funct. Anal. 3 (1993) 502-526.
9. [9] Talagrand M., Lower classes for fractional Brownian motion, J. Th. Probab. 9 (1996) 191-213.