Sharp Small Deviation Asymptotics in the L 2-Norm for a Class of Gaussian Processes

Author:

Nikitin Ya. Yu.,Kharinski P. A.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Mathematics,Statistics and Probability

Reference20 articles.

1. IMS Lect. Notes Monograph Series;R. Adler,1990

2. L. Beghin, Ya. Yu. Nikitin, and E. Orsingher, “Exact small ball constants for some Gaussian processes under the L 2-norm,” Zap. Nauchn. Semin. POMI, 298, 5–21 (2003).

3. P. Deheuvels and G. Martynov, “The Karhunen-Loeve expansions for weighted Wiener processes and Brownian bridges via Bessel functions,” in: Progress of Probability, Vol. 55, Birkhauser (2003), pp. 57–93.

4. P. Deheuvels and G. Martynov, “The Karhunen-Loeve decomposition of a Gaussian process generated by independent pairs of exponential random variables,” Ann. Statist. (2005) (submitted).

5. R. M. Dudley, J. Hoffmann-Jorgensen, and L. A. Shepp, “On the lower tail of Gaussian seminorms,” Ann. Prob., 7, 319–342 (1979).

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