On the comparison of the distribution of the supremum of random fields represented by stochastic integrals
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In this paper we compare the distribution of the supremum of the Gaussian random fields Z(P) = ∫ Cp G(P, P′) dW(P′) and U(P) = ∫ Cp dW(P'), where CP are circles of fixed radius, dW is a white noise field and G are special deterministic response functions. The results obtained permit us to establish upper bounds for the distribution of the supremum of Z(P) by applying some well-known inequalities on U(P). The comparison of the suprema is carried out also, when C P = ℝ2, between fields with different response functions.
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1987 ◽
Vol 24
(03)
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pp. 574-585
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2019 ◽
Vol 30
(01)
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pp. 181-223
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2008 ◽
Vol 59
(2)
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pp. 203-232
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1990 ◽
Vol 119
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pp. 93-106
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