## The Annals of Probability

### Validity of the expected Euler characteristic heuristic

#### 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 fx, derived from the original process f.

#### Article information

Source
Ann. Probab., Volume 33, Number 4 (2005), 1362-1396.

Dates
First available in Project Euclid: 1 July 2005

https://projecteuclid.org/euclid.aop/1120224584

Digital Object Identifier
doi:10.1214/009117905000000099

Mathematical Reviews number (MathSciNet)
MR2150192

Zentralblatt MATH identifier
1083.60031

#### Citation

Taylor, Jonathan; Takemura, Akimichi; Adler, Robert J. Validity of the expected Euler characteristic heuristic. Ann. Probab. 33 (2005), no. 4, 1362--1396. doi:10.1214/009117905000000099. https://projecteuclid.org/euclid.aop/1120224584

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