{"paper":{"title":"On recurrence and transience of multivariate near-critical stochastic processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\\"otz Kersting","submitted_at":"2016-05-13T06:58:07Z","abstract_excerpt":"We obtain complementary recurrence and transience criteria for processes $X=(X_n)_{n \\ge 0}$ with values in $\\mathbb R^d_+$ fulfilling a non-linear equation $X_{n+1}=MX_n+g(X_n)+ \\xi_{n+1}$. Here $M$ denotes a primitive matrix having Perron-Frobenius eigenvalue 1, and $g$ denotes some function. The conditional expectation and variance of the noise $(\\xi_{n+1})_{n \\ge 0}$ are such that $X$ obeys a weak form of the Markov property. The results generalize criteria for the 1-dimensional case in [5]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04064","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"}