Validity of the expected Euler characteristic heuristic

• 成果类型: Article
• 署名作者: Taylor, J; Takemura, A; Adler, RJ
• 署名单位: Stanford University; University of Tokyo; Technion Israel Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000099
• 发表日期: 2005
• 页码: 1362-1396
• 关键词: gaussian fields; excursion sets; maximum; tube; geometry; volume

摘要

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.