{"paper":{"title":"Asymptotics of random processes with immigration II: convergence to stationarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Iksanov, Alexander Marynych, Matthias Meiners","submitted_at":"2013-11-27T10:38:41Z","abstract_excerpt":"Let $X_1, X_2,\\ldots$ be random elements of the Skorokhod space $D(\\mathbb{R})$ and $\\xi_1, \\xi_2, \\ldots$ positive random variables such that the pairs $(X_1,\\xi_1), (X_2,\\xi_2),\\ldots$ are independent and identically distributed. We call the random process $(Y(t))_{t \\in \\mathbb{R}}$ defined by $Y(t):=\\sum_{k \\geq 0}X_{k+1}(t-\\xi_1-\\ldots-\\xi_k)1_{\\{\\xi_1+\\ldots+\\xi_k\\leq t\\}}$, $t\\in\\mathbb{R}$ random process with immigration at the epochs of a renewal process. Assuming that $X_k$ and $\\xi_k$ are independent and that the distribution of $\\xi_1$ is nonlattice and has finite mean we investiga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6923","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"}