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Excursions above a fixed level by n-dimensional random fields

Published online by Cambridge University Press:  14 July 2016

Robert J. Adler
Robert J. Adler*
Affiliation:
University of New South Wales
*
*Currently visiting Tel-Aviv University on a C.S.I.R.O. post-doctoral fellowship.
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Abstract

For an n-dimensional random field X(t) we define the excursion set A of X(t) by A = [t ∊ S: X(t) ≧ u] for real u and compact S ⊂ Rn. We obtain a generalisation of the number of upcrossings of a one-dimensional stochastic process to random fields via a characteristic of the set A related to the Euler characteristic of differential topology. When X(t) is a homogeneous Gaussian field satisfying certain regularity conditions we obtain an explicit formula for the mean value of this characteristic.

Keywords

RANDOM FIELDSEXCURSION SETSEULER CHARACTERISTICHOMOGENEOUS GAUSSIAN PROCESSMEAN VALUES
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 276 - 289
Copyright
Copyright © Applied Probability Trust 1976 

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