{"paper":{"title":"Heat kernel and ergodicity of SDEs with distributional drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Guohuan Zhao, Xicheng Zhang","submitted_at":"2017-10-28T23:47:30Z","abstract_excerpt":"In this paper we consider the following SDE with distributional drift $b$: $$ {\\rm d} X_t=\\sigma(X_t){\\rm d} B_t+b(X_t){\\rm d} t,\\ X_0=x\\in{\\mathbb R}^d, $$ where $\\sigma$ is a bounded continuous and uniformly non-degenerate $d\\times d$-matrix-valued function, $B$ is a $d$-dimensional standard Brownian motion. Let $\\alpha\\in(0,\\frac{1}{2}]$, $p\\in(\\frac{d}{1-\\alpha},\\infty)$ and $\\beta\\in[\\alpha,1]$, $q\\in(\\frac{d}{\\beta},\\infty)$. Assume $\\|({\\mathbb I}-\\Delta)^{-\\alpha/2}b\\|_p+\\|(-\\Delta)^{\\beta/2}\\sigma\\|_q<\\infty$. We show the existence and uniqueness of martingale solutions to the above S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10537","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"}