ON A GENERAL KAC-RICE FORMULA FOR THE MEASURE OF A LEVEL SET

• 成果类型: Article
• 署名作者: Armentano, Diego; Azais, Jean-m arc; Leon, Jose afael
• 署名单位: Universidad de la Republica, Uruguay; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universidad de la Republica, Uruguay
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2158
• 发表日期: 2025
• 页码: 1828-1851
• 关键词: perimeter; number

摘要

Let X() be a random field from R-D to R-d, where D >= d. We study the level set X-1(u), where u is an element of R-d. Specifically, we provide a weak condition for this level set to be rectifiable. Next, we establish the Kac-Rice formula to compute the (D-d)-dimensional Hausdorff measure. Our results extend previous work, particularly in the non-Gaussian case where we obtain a very general result. We conclude with several extensions and examples of applications, including functions of Gaussian random fields, zeros of the likelihood functions, gravitational microlensing, and shot-noise.