{"paper":{"title":"Spatial Risk Measure for Max-Stable and Max-Mixture Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Ahmed Manaf (ICJ), C\\'eline Vial (ICJ, DRACULA), Pierre Ribereau (ICJ), V\\'eronique Maume-Deschamps (ICJ)","submitted_at":"2017-06-26T06:33:09Z","abstract_excerpt":"In this paper, we consider isotropic and stationary max-stable, inverse max-stable and max-mixture processes $X=(X(s))\\_{s\\in\\bR^2}$ and the damage function $\\cD\\_X^{\\nu}= |X|^\\nu$ with $0<\\nu<1/2$. We study the quantitative behavior of a risk measure which is the variance of the average of $\\cD\\_X^{\\nu}$ over a region $\\mathcal{A}\\subset \\bR^2$.} This kind of risk measure has already been introduced and studied for \\vero{some} max-stable processes in \\cite{koch2015spatial}. %\\textcolor{red}{In this study, we generalised this risk measure to be applicable for several models: asymptotic depende"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08244","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"}