{"paper":{"title":"A continuum-tree-valued Markov process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Delmas (CERMICS), Romain Abraham (MAPMO)","submitted_at":"2009-04-27T14:44:11Z","abstract_excerpt":"We present a construction of a L\\'evy continuum random tree (CRT) associated with a super-critical continuous state branching process using the so-called exploration process and a Girsanov's theorem. We also extend the pruning procedure to this super-critical case. Let $\\psi$ be a critical branching mechanism. We set $\\psi_\\theta(\\cdot)=\\psi(\\cdot+\\theta)-\\psi(\\theta)$. Let $\\Theta=(\\theta_\\infty,+\\infty)$ or $\\Theta=[\\theta_\\infty,+\\infty)$ be the set of values of $\\theta$ for which $\\psi_\\theta$ is a branching mechanism. The pruning procedure allows to construct a decreasing L\\'evy-CRT-value"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4175","kind":"arxiv","version":3},"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"}