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When $r\\to\\infty$, both ${}^{(r)}X_t \\to 0$ and $\\Delta_t^{(r)} \\to 0$ a.s. for each $t>0$, and it is interesting to study the weak limiting behaviour of $\\bigl({}^{(r)}X_t, \\Delta_t^{(r)}\\bigr)$ in this case. We term this \"large-trimming\" behaviour. Concentrating on the case $t=1$, we study joint convergence of $\\bigl({}^{(r)}X_1, \\Delta_1^{(r)}"},"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":"1802.09814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-27T10:41:40Z","cross_cats_sorted":[],"title_canon_sha256":"95db2f11c9c8858a313c5461ecc71620b4eaa35c8e9787103d6c073a820b9bd4","abstract_canon_sha256":"9f744f77972748e8560479666824e48e4a92066eca3cad4568589a18a826b206"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:22.115718Z","signature_b64":"7OaYcPF5+m+ffaiorgLv0tfJuvAdMT7YlOTgCUY7eTmiak5wcm9azrPocaORXWiHcxfJQUmaxfZU41ryUOxZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ce5013b93d461ea3701902c66373f529f5d26640e0df076869898edc9381207","last_reissued_at":"2026-05-18T00:22:22.115208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:22.115208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trimmed L\\'evy Processes and their Extremal Components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross Maller, Sidney Resnick, Yuguang Ipsen","submitted_at":"2018-02-27T10:41:40Z","abstract_excerpt":"We analyse a trimmed stochastic process of the form ${}^{(r)}X_t= X_t - \\sum_{i=1}^r \\Delta_t^{(i)}$, where $(X_t)_{t \\geq 0}$ is a driftless subordinator on $\\mathbb{R}$ with its jumps on $[0,t]$ ordered as $ \\Delta_t^{(1)}\\ge \\Delta_t^{(2)} \\cdots$. When $r\\to\\infty$, both ${}^{(r)}X_t \\to 0$ and $\\Delta_t^{(r)} \\to 0$ a.s. for each $t>0$, and it is interesting to study the weak limiting behaviour of $\\bigl({}^{(r)}X_t, \\Delta_t^{(r)}\\bigr)$ in this case. We term this \"large-trimming\" behaviour. 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