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A relaxation of conditions for the convergence of the maximum of stationary random field to an extreme value distribution

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  • Nakajima, Kazuki

Abstract

Stehr and Rønn-Nielsen (2021) studies a stationary random field on Zd and obtains that, under some conditions, the normalized version of the distribution of the maximum of the field over an increasing sequence of index sets converges to an extreme value distribution. We consider the increase rate of index sets imposed in their paper. The main purpose of this paper is to relax their conditions. We also investigate what occurs in more general cases.

Suggested Citation

  • Nakajima, Kazuki, 2026. "A relaxation of conditions for the convergence of the maximum of stationary random field to an extreme value distribution," Statistics & Probability Letters, Elsevier, vol. 236(C).
    • Handle: RePEc:eee:stapro:v:236:y:2026:i:c:s0167715226001380
    DOI: 10.1016/j.spl.2026.110774
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