{"paper":{"title":"Kinetic SDEs with subcritical distributional drifts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xicheng Zhang, Zikai Chen, Zimo Hao","submitted_at":"2025-08-17T04:31:01Z","abstract_excerpt":"In this paper we study the well-posedness of the kinetic stochastic differential equation (SDE) in $\\mathbb R^{2d}(d\\geq2)$ driven by Brownian motion: $$\\mathord{{\\rm d}} X_t=V_t\\mathord{{\\rm d}} t,\\ \\mathord{{\\rm d}} V_t=b(t,X_t,V_t)\\mathord{{\\rm d}} t+\\sqrt{2}\\mathord{{\\rm d}} W_t,$$ where the subcritical distribution-valued drift $b$ belongs to the weighted anisotropic H\\\"{o}lder space $\\mathbb L_T^{q_b}\\mathbf C_{\\boldsymbol{a}}^{\\alpha_b}(\\rho_\\kappa)$ with parameters $\\alpha_b\\in(-1,0)$, $q_b\\in(\\frac{2}{1+\\alpha_b},\\infty]$, $\\kappa\\in[0,1+\\alpha_b)$ and $\\div_v b$ is bounded. We establ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.12234","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.12234/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"}