{"paper":{"title":"On Extremal Index of max-stable stationary processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzysztof D\\k{e}bicki","submitted_at":"2017-04-05T17:57:29Z","abstract_excerpt":"In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary process $W(t),t\\in R$ as $$\\mathcal{H}_W^\\delta= \\lim_{T\\to\\infty} T^{-1} E{ \\left(\\sup_{t\\in \\delta Z \\cap [0,T]} e^{W(t)}\\right) },\\ \\delta \\ge 0$$ (set $0 Z=R$ if $\\delta=0$) and the extremal index of the associated max-stable stationary process $\\xi_W$. We derive several new formulas and obtain lower bounds for $\\mathcal{H}_W^\\delta$ if $W$ is a Gaussian or a L\\'evy process. As a by-product we show an interesting relation between Pickands constants and lower tail probab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01563","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}