{"paper":{"title":"On quasi-ergodic distribution for one-dimensional diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guoman He, Hanjun Zhang","submitted_at":"2014-09-29T12:21:51Z","abstract_excerpt":"In this paper, we study quasi-ergodicity for one-dimensional diffusion $X$ killed at 0, when 0 is an exit boundary and $+\\infty$ is an entrance boundary. Using the spectral theory tool, we show that if the killed semigroup is intrinsically ultracontractive, then there exists a unique quasi-ergodic distribution for $X$. An example is given to illustrate the result. Moreover, the ultracontractivity of the killed semigroup is also studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8094","kind":"arxiv","version":4},"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"}