Chapter

Random Fields and Geometry

Part of the series Springer Monographs in Mathematics pp 75-99

Excursion Probabilities

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Abstract

As we have already mentioned more than once before, one of the oldest and most important problems in the study of stochastic processes of any kind is to evaluate the excursion probabilities
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where f is a random process over some parameter set T . As usual, we shall restrict ourselves to the case in which f is centered and Gaussian and T is compact for the canonical metric of (1.3.1).