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 $P\; \{sup$_{t Î T} X(t) > u}, where $X(t)$ is a Gaussian random field with a compact parameter set in the space $lp$, £ 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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