{"paper":{"title":"Max-stable processes and stationary systems of L\\'evy particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sebastian Engelke, Zakhar Kabluchko","submitted_at":"2014-12-23T16:58:36Z","abstract_excerpt":"We study stationary max-stable processes $\\{\\eta(t)\\colon t\\in\\mathbb R\\}$ admitting a representation of the form $\\eta(t)=\\max_{i\\in\\mathbb N}(U_i+ Y_i(t))$, where $\\sum_{i=1}^{\\infty} \\delta_{U_i}$ is a Poisson point process on $\\mathbb R$ with intensity ${\\rm e}^{-u} {\\rm d} u$, and $Y_1,Y_2,\\ldots$ are i.i.d.\\ copies of a process $\\{Y(t)\\colon t\\in\\mathbb R\\}$ obtained by running a L\\'evy process for positive $t$ and a dual L\\'evy process for negative $t$. We give a general construction of such L\\'evy-Brown-Resnick processes, where the restrictions of $Y$ to the positive and negative half-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7444","kind":"arxiv","version":2},"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"}