Open Access
Translator Disclaimer
July 2005 Validity of the expected Euler characteristic heuristic
Jonathan Taylor, Akimichi Takemura, Robert J. Adler
Ann. Probab. 33(4): 1362-1396 (July 2005). DOI: 10.1214/009117905000000099


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.


Download Citation

Jonathan Taylor. Akimichi Takemura. Robert J. Adler. "Validity of the expected Euler characteristic heuristic." Ann. Probab. 33 (4) 1362 - 1396, July 2005.


Published: July 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1083.60031
MathSciNet: MR2150192
Digital Object Identifier: 10.1214/009117905000000099

Primary: 53A17 , 58A05 , 60G15 , 60G60
Secondary: 60G17 , 60G70 , 62M40

Keywords: Euler characteristic , Excursions , Gaussian processes , Manifolds , Point processes , Random fields , volume of tubes

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 4 • July 2005
Back to Top