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Large deviations for Gaussian processes in the Hölder norm. (English. Russian original) Zbl 1064.60045

Izv. Math. 67, No. 5, 1061-1079 (2003); translation from Izv. Ross. Akad. Nauk Ser. Mat. 67, No. 5, 207-224 (2003).
Summary: Some results are proved on the exact asymptotic representation of large deviation probabilities for Gaussian processes in the Hölder norm. The following classes of processes are considered: the Wiener process, the Brownian bridge, fractional Brownian motion, and stationary Gaussian processes with power-law covariance function. The investigation uses the method of double sums for Gaussian fields.

MSC:

60F10 Large deviations
60G15 Gaussian processes
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