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On sojourn measures above a moving barrier for a Gaussian field with long-range dependence. (English. Ukrainian original) Zbl 0958.60035
Theory Probab. Math. Stat. 59, 47-56 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 47-56 (1998).
Many problems in the theory of turbulence, meteorology, statistical radiophysics may be reduced to the limit theorems for functionals of random fields. The author considers the limit distributions of functionals which are measures of sets formed by some cylinders. The main attention is paid to Gaussian random fields for which an integral of the correlation function is finite. The author uses ideas from his previous paper [Random Oper. Stoch. Equ. 1, No. 3, 213-222 (1993; Zbl 0839.60045)].
MSC:
60G15 Gaussian processes
60G60 Random fields
60H05 Stochastic integrals
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