{"paper":{"title":"Extremes of multidimensional Gaussian processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kamil Marcin Kosi\\'nski, Krzysztof D\\k{e}bicki, Michel Mandjes, Tomasz Rolski","submitted_at":"2010-05-31T22:35:52Z","abstract_excerpt":"This paper considers extreme values attained by a centered, multidimensional Gaussian process $X(t)= (X_1(t),\\ldots,X_n(t))$ minus drift $d(t)=(d_1(t),\\ldots,d_n(t))$, on an arbitrary set $T$. Under mild regularity conditions, we establish the asymptotics of \\[\\log\\mathbb P\\left(\\exists{t\\in T}:\\bigcap_{i=1}^n\\left\\{X_i(t)-d_i(t)>q_iu\\right\\}\\right),\\] for positive thresholds $q_i>0$, $i=1,\\ldots,n$, and $u\\to\\infty$. Our findings generalize and extend previously known results for the single-dimensional and two-dimensional cases. A number of examples illustrate the theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0029","kind":"arxiv","version":4},"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"}