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We derive asymptotic expansion of $\\mathcal{P}_S(u,T_u)$, as $u\\to\\infty$, for the aggregate claim process $X$ modeled by Gaussian processes. As a by-product, we derive the exact tail asymptotics of the infimum of a stand"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.07061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-27T12:43:21Z","cross_cats_sorted":[],"title_canon_sha256":"27503a06aea3016bdf89beb09bb3b6c35448a5b0d2ce66e83521d61b7b54e8a5","abstract_canon_sha256":"6ccf42401caeeeed3c63a30e92aa9afb1c570b09be72f9d07f27ffd7c8393ae1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:50.745054Z","signature_b64":"63fmInxw++XhhC5QnlJiC6MQ5UKbt44O9gYrBKP30XdCghIGgEOAA7ODKodtFJWw7UmUNhyONy1TA4SRDtPFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"667f055fbb55bdc9567836b958bd4f0678eae93cfbab9abced9eafc93c148f0d","last_reissued_at":"2026-05-18T01:16:50.744350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:50.744350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Parisian ruin over a finite-time horizon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzysztof Debicki, Lanpeng Ji","submitted_at":"2015-04-27T12:43:21Z","abstract_excerpt":"For a risk process $R_u(t)=u+ct-X(t), t\\ge 0$, where $u\\ge 0$ is the initial capital, $c>0$ is the premium rate and $X(t),t\\ge 0$ is an aggregate claim process, we investigate the probability of the Parisian ruin \\[ \\mathcal{P}_S(u,T_u)=\\mathbb{P}\\{\\inf_{t\\in[0,S]} \\sup_{s\\in[t,t+T_u]} R_u(s)<0\\}, \\] with a given positive constant $S$ and a positive measurable function $T_u$. We derive asymptotic expansion of $\\mathcal{P}_S(u,T_u)$, as $u\\to\\infty$, for the aggregate claim process $X$ modeled by Gaussian processes. 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