{"paper":{"title":"Almost sure growth of supercritical multi-type continuous state branching process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas E. Kyprianou, Sandra Palau, Yan-Xia Ren","submitted_at":"2017-07-16T22:33:27Z","abstract_excerpt":"In Li (2011), Example 2.2, the notion of a multi-type continuous-state branching process (MCSBP) was introduced with a finite number of types, with the countably infinite case being proposed in Kyprianou and Palau (2017). One may consider such processes as a super-Markov chain on a countable state-space of types, which undertakes both local and non-local branching. In Kyprianou and Palau (2017) it was shown that, for MCSBPs, under mild conditions, there exists a lead eigenvalue which characterises the spectral radius of the linear semigroup associated to the process. Moreover, in a qualitative"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04955","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"}