{"paper":{"title":"Birth and death process with one-side bounded jumps in random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hua-Ming Wang","submitted_at":"2014-07-12T13:42:41Z","abstract_excerpt":"Let $\\omega=(\\omega_i)_{i\\in\\mathbb Z}=(\\mu^{L}_i,...,\\mu^{1}_i,\\lambda_i)_{i\\in \\mathbb Z}$, which serves as the environment, be a sequence of i.i.d. random nonnegative vectors, with $L\\ge1$ a positive integer. We study birth and death process $N_t$ which, given the environment $\\omega,$ waits at a state $n$ an exponentially distributed time with parameter $\\lambda_n+\\sum_{l=1}^L\\mu^{l}_n$ and then jumps to $n-i$ with probability ${\\mu^i_n}/(\\lambda_n+\\sum_{l=1}^L\\mu^{l}_n),$ $i=1,...,L$ or to $n+1$ with probability ${\\lambda_n}/(\\lambda_n+\\sum_{l=1}^L\\mu^{l}_n).$ A sufficient condition for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3385","kind":"arxiv","version":1},"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"}