{"paper":{"title":"On the survival of a class of subcritical branching processes in random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Vincent Bansaye (CMAP), Vladimir Vatutin","submitted_at":"2013-07-15T14:31:24Z","abstract_excerpt":"Let $Z_{n}$ be the number of individuals in a subcritical BPRE evolving in the environment generated by iid probability distributions. Let $X$ be the logarithm of the expected offspring size per individual given the environment. Assuming that the density of $X$ has the form $$p_{X}(x)=x^{-\\beta -1}l_{0}(x)e^{-\\rho x}$$ for some $\\beta >2,$ a slowly varying function $l_{0}(x)$ and $\\rho \\in \\left( 0,1\\right),$ we find the asymptotic survival probability and prove a Yaglom type conditional limit theorem for the process. The survival probability decreases exponentially with an additional polynomi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3963","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"}