{"paper":{"title":"A general continuous-state nonlinear branching process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pei-Sen Li, Xiaowen Zhou, Xu Yang","submitted_at":"2017-08-04T15:44:47Z","abstract_excerpt":"In this paper we consider the unique nonnegative solution to the following generalized version of the stochastic differential equation for a continuous-state branching process. \\beqnn X_t \\ar=\\ar x+\\int_0^t\\gamma_0(X_s)\\dd s+\\int_0^t\\int_0^{\\gamma_1(X_{s-})} W(\\dd s,\\dd u)\\cr \\ar\\ar\\qquad+\\int_0^t\\int_{0}^\\infty\\int_0^{\\gamma_2(X_{s-})} z\\tilde{N}(\\dd s, \\dd z, \\dd u), \\eeqnn where $W(\\dd t,\\dd u) $ and $\\tilde{N}(\\dd s, \\dd z, \\dd u)$ denote a Gaussian white noise and an independent compensated spectrally positive Poisson random measure, respectively, and $\\gamma_0,\\gamma_1$ and $\\gamma_2$ ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01560","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"}