Validity of the expected Euler characteristic heuristic

Preprint

21 July 2005

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0507442

Abstract

We study the accuracy of the expected Euler characteristic approximation to the distribution of the maximum of a smooth, centered, unit variance Gaussian process f. Using a point process representation of the error, valid for arbitrary smooth processes, we show that the error is in general exponentially smaller than any of the terms in the approximation. We also give a lower bound on this exponential rate of decay in terms of the maximal variance of a family of Gaussian processes f^x, derived from the original process f.

Keywords

EXPECTED EULER CHARACTERISTIC
DISTRIBUTION OF THE MAXIMUM
CHARACTERISTIC HEURISTIC
GAUSSIAN PROCESS
APPROXIMATION
POINT PROCESS
HEURISTIC

All Related Versions

Version 1, 2005-07-21, ArXiv
Published version: The Annals of Probability, 33 (4), 1362.

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