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Asymptotic crossing rates for stationary Gaussian vector processes. (English) Zbl 0648.60044
The expected number of crossings of a differentiable Gaussian vector process through a hypersurface is given by a surface integral over this surface. Simple asymptotic approximations for these integrals are derived. The results are obtained by a generalization of the Laplace method for the asymptotic expansion of multidimensional integrals. With these formulas approximations for the extreme value distribution of functions of vector processes can be found.
Reviewer: K.Breitung

MSC:
60G15 Gaussian processes
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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