Evaluating the small deviation probabilities for subordinated Lévy processes

Stochastic Processes and their Applications

Volumn 113, Issue 2, 2004, Pages 273-287

  Linde, Werner ^a   Shi, Zhan ^b  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Fractional Brownian motion; L vy process; Small deviation; Subordination

Indexed keywords

EID: 4544297219     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2004.04.001     Document Type: Article

References (19)

1. Anderson T.W. The integral of symmetric unimodular functions over a symmetric convex set and some probability inequalities Proc. Amer. Math. Soc. 6 1955 170-176
2. J. Bertoin Subordinators: examples and applications, in: P. Bernard (Ed.), Ecole d'Eté St.-Flour 1997, Lecture Notes in Mathematics, Vol. 1717, Springer, Berlin, 1999, pp. 1-91
3. Y. Ishikawa Small deviations property and its application, in: Second MaPhySto Conference on Lévy Processes: Theory and Application, Vol. 22, MaPhySto Publ., Aarhus, 2002, pp. 149-154
4. Kuelbs J. Li W.V. Metric entropy and the small ball problem for Gaussian measures J. Funct. Anal. 116 1993 133-157
5. M. Ledoux Isoperimetry and Gaussian analysis, Lectures on Probability Theory and Statistics (St-Flour, 1994), Lecture Notes in Mathematics, Vol. 1648, Springer, Berlin, 1996, pp. 165-294
6. Li W.V. Linde W. Existence of small ball constants for fractional Brownian motions C. R. Acad. Sci. Paris Sér. I Math. 326 1998 1329-1334
7. Li W.V. Linde W. Approximation, metric entropy and small ball estimates for Gaussian measures Ann. Probab. 27 1999 1556-1578
8. Li W.V. Linde W. Small deviations of stable processes via metric entropy J. Theoret. Probab. 17 2004 261-284
9. Li W.V. Shao Q.-M. Gaussian processes: inequalities, small ball probabilities and applications in: Rao C.R. Shanbhag D. (Eds.) Stochastic Processes: Theory and Methods, Handbook of Statistics, Vol. 19 2001 533-597 North-Holland Amsterdam
10. M.A. Lifshits Asymptotic behavior of small ball probabilities, in: Proceedings of the Seventh Vilnius Conference on Probability Theory and Mathematical Statistics, VSP/TEV, Vilnius, 1999, pp. 453-468
11. M.A. Lifshits T. Simon Small deviations for fractional stable processes, Ann. Inst. H. Poincaré Probab. Statist
12. Rosinski J. On a class of infinitely divisible processes represented as mixtures of Gaussian processes in: Cambanis S. et al. (Eds.) Stable Processes and Related Topics 1991 27-41 Birkhäuser Boston, MA
13. Samorodnitsky G. Lower tails of self-similar stable processes Bernoulli 4 1998 127-142
14. Samorodnitsky G. Taqqu M.S. Stable Non-Gaussian Random Processes 1994 Chapman & Hall New York
15. Sato K. Lévy Processes and Infinitely Divisible Distributions 1999 Cambridge University Press Cambridge
16. Simon T. Sur les petites déviations d'un processus de Lévy Potential Anal. 14 2001 155-173
17. T. Simon Small ball estimates in p-variation for stable processes, 2003 (preprint)
18. Talagrand M. New Gaussian estimates for enlarged balls Geom. Funct. Anal. 3 1993 502-526
19. Taylor S.J. Sample path properties of a transient stable process J. Math. Mech. 16 1967 1229-1246