Tube formula for spherically contoured random fields with subexponential marginals

Satoshi Kuriki and Evgeny Spodarev

Stochastic Processes and their Applications, 2026, vol. 195, issue C

Abstract: It is widely known that the tube method, or equivalently the Euler characteristic heuristic, provides a very accurate approximation for the tail probability that the supremum of a smooth Gaussian random field exceeds a threshold value c. The relative approximation error Δ(c) is exponentially small as a function of c when c tends to infinity. On the other hand, little is known about non-Gaussian random fields.

Keywords: Bonferroni approximation; Critical radius; Euler characteristic heuristic; Multivariate Mills’ ratio; Regularly varying tails; Simultaneous inference; Sub-Gaussian random field; Upper tail dependence coefficient (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104858

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