{"paper":{"title":"Non-markovian limits of additive functionals of Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Milton Jara, Tomasz Komorowski","submitted_at":"2009-05-13T18:31:52Z","abstract_excerpt":"In this paper we consider an additive functional of an observable $V(x)$ of a Markov jump process. We assume that the law of the expected jump time $t(x)$ under the invariant probability measure $\\pi$ of the skeleton chain belongs to the domain of attraction of a subordinator. Then, the scaled limit of the functional is a Mittag-Leffler proces, provided that $\\Psi(x):=V(x)t(x)$ is square integrable w.r.t. $\\pi$. When the law of $\\Psi(x)$ belongs to a domain of attraction of a stable law the resulting process can be described by a composition of a stable process and the inverse of a subordinato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2163","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"}