{"paper":{"title":"On general skew Brownian motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Liping Li","submitted_at":"2018-12-20T08:33:34Z","abstract_excerpt":"The aim of this paper is two-fold. On one hand, we will study the distorted Brownian motion on $\\mathbb{R}$, i.e. the diffusion process $X$ associated with a regular and strongly local Dirichlet form obtained by the closure of $\\mathscr{E}(f,g)=\\frac{1}{2}\\int_\\mathbb{R} f'(x)g'(x)\\rho(x)dx$ for $f,g\\in C_c^\\infty(\\mathbb{R})$ on $L^2(\\mathbb{R}, \\mathfrak{m})$, where $\\mathfrak{m}(dx)=\\rho(x)dx$ and $\\rho$ is a certain positive function. After figuring out the irreducible decomposition of $X$, we will present a characterization of that $X$ becomes a semi-martingale by virtue of so-called Fuku"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08415","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"}