{"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. Concentrating on the case $t=1$, we study joint convergence of $\\bigl({}^{(r)}X_1, \\Delta_1^{(r)}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09814","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"}