FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1996, VOLUME 2, NUMBER 4, PAGES 1117-1141

The double sum method for Gaussian fields with a parameter set in lp

V. R. Fatalov

Abstract

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In the paper it is presented a method to compute asymptotics of the probability P {supt Î T X(t) > u}, where X(t) is a Gaussian random field with a compact parameter set in the space lp, 1 < p £ 2. On the basis of obtained result it is found the exact asymptotics of tail distribution for the supremum of lq-norm of lq-valued Ornstein--Uhlenbeck process when q > 2.

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