{"paper":{"title":"Small-time approximation of the transition density for diffusions with singularities. Application to the Wright-Fisher model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"stat.ME","authors_text":"Gerardo Mart\\'inez, Jos\\'e Le\\'on, Mar\\'ia In\\'es Fariello, Tania Roa","submitted_at":"2022-12-22T01:21:50Z","abstract_excerpt":"The Wright-Fisher (W-F) diffusion model serves as a foundational framework for interpreting population evolution through allele frequency dynamics over time. Despite the known transition probability between consecutive generations, an exact analytical expression for the transition density at arbitrary time intervals remains elusive. Commonly utilized distributions such as Gaussian or Beta inadequately address the fixation issue at extreme allele frequencies (0 or 1), particularly for short periods. In this study, we introduce two alternative parametric functions, namely the Asymptotic Expansio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11442","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.11442/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}