{"paper":{"title":"Quantitative heat kernel estimates for diffusions with distributional drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nicolas Perkowski, Willem van Zuijlen","submitted_at":"2020-09-22T19:53:41Z","abstract_excerpt":"We consider the stochastic differential equation on $\\mathbb{R}^d$ given by $$ \\, \\mathrm{d}X_t = b(t,X_t) \\, \\mathrm{d}t + \\, \\mathrm{d} B_t, $$ where $B$ is a Brownian motion and $b$ is considered to be a distribution of regularity $ > -\\frac12$. We show that the martingale solution of the SDE has a transition kernel $\\Gamma_t$ and prove upper and lower heat kernel bounds for $\\Gamma_t$ with explicit dependence on $t$ and the norm of $b$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.10786","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"}