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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.3963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-15T14:31:24Z","cross_cats_sorted":[],"title_canon_sha256":"23b82e5f4a6c6a7a4034eb2a5b434654df42b0acc24bb1e4d97fd96561d55b2d","abstract_canon_sha256":"e8471f9ed1dd33b26e84c5e8781aa013a13f2115e0b9dcabd3cebde0cf07650e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:15.290787Z","signature_b64":"ewtuQ2dgSjo6DCC1nFc3X3Q6K+wCUi7fPe/Hx6BVNnvIiKVtkWJOPXj9VhVhzefvkbL3bFIqWSGHjrgsS6pTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1840984cfc9f431e02b78dc9c0f57593a095b904fcb5575f375e57f151fa0a2a","last_reissued_at":"2026-05-18T03:04:15.290141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:15.290141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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