{"paper":{"title":"Complete Bernstein functions and subordinators with nested ranges. A note on a paper by P. Marchal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chang-song Deng, Ren\\'e L. Schilling","submitted_at":"2016-06-15T01:30:35Z","abstract_excerpt":"Let $\\alpha:[0,1]\\to [0,1]$ be a measurable function. It was proved by P. Marchal \\cite{Mar15} that the function\n  $$\n  \\phi^{(\\alpha)}(\\lambda):=\\exp\\left[\n  \\int_0^1\\frac{\\lambda-1}{1+(\\lambda-1)x}\\,\\alpha(x)\\,d x\n  \\right],\\quad \\lambda>0\n  $$ is a special Bernstein function. Marchal used this to construct, on a single probability space, a family of regenerative sets $\\mathcal R^{(\\alpha)}$ such that $\\mathcal{R}^{(\\alpha)} \\stackrel{\\text{law}}{=} \\overline{\\{S^{(\\alpha)}_t:t\\geq 0\\}}$ ($S^{(\\alpha)}$ is the subordinator with Laplace exponent $\\phi^{(\\alpha)}$) and $\\mathcal R^{(\\alpha)}\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04610","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"}