{"paper":{"title":"Extremes and Limit Theorems for Difference of Chi-type processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"C. Ling, E. Hashorva, L. Ji, P. Albin","submitted_at":"2015-08-11T21:41:04Z","abstract_excerpt":"Let $\\{\\zeta_{m,k}^{(\\kappa)}(t), t \\ge0\\}, \\kappa>0$ be random processes defined as the differences of two independent stationary chi-type processes with $m$ and $k$ degrees of freedom. In applications such as physical sciences and engineering dealing with structure reliability, of interest is the approximation of the probability that the random process $\\zeta_{m,k}^{(\\kappa)}$ stays in some safety region up to a fixed time $T$. In this paper we derive the asymptotics of $\\mathbb{P}\\{\\sup_{t\\in[0, T]}\\zeta_{m,k}^{(\\kappa)}(t)> u\\}, {u\\to\\infty}$ under some assumptions on the covariance struct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02758","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"}