{"paper":{"title":"The Fundamental Solution to One-Dimensional Degenerate Diffusion Equation, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Ian Weih-Wadman, Linan Chen","submitted_at":"2019-05-29T20:43:46Z","abstract_excerpt":"In this work we adopt a combination of probabilistic approach and analytic methods to study the fundamental solutions to variations of the Wright-Fisher equation in one dimension. To be specific, we consider a diffusion equation on $\\left(0,\\infty\\right)$ whose diffusion coefficient vanishes at the boundary 0, equipped with the Cauchy initial data and the Dirichlet boundary condition. One type of diffusion operator that has been extensively studied is the one whose diffusion coefficient vanishes linearly at 0. Our main goal is to extend the study to cases when the diffusion coefficient has a g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12716","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"}