{"paper":{"title":"Weak uniqueness for singular stochastic equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Leonid Mytnik, Oleg Butkovsky","submitted_at":"2024-05-22T16:08:00Z","abstract_excerpt":"We put forward a new method for proving weak uniqueness of stochastic equations with singular drifts driven by a non-Markov or infinite-dimensional noise. We apply our method to study stochastic heat equation (SHE) driven by Gaussian space-time white noise $$ \\frac{\\partial}{\\partial t} u_t(x)=\\frac12 \\frac{\\partial^2}{\\partial x^2}u_t(x)+b(u_t(x))+\\dot{W}_{t}(x), \\quad t>0,\\, x\\in D\\subset\\mathbb{R}, $$ and multidimensional stochastic differential equation (SDE) driven by fractional Brownian motion with the Hurst index $H\\in(0,1/2)$ $$ d X_t=b(X_t) dt +d B_t^H,\\quad t>0. $$ In both cases $b$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.13780","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/2405.13780/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"}