{"paper":{"title":"Existence of flows for linear Fokker-Planck-Kolmogorov equations and its connection to well-posedness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marco Rehmeier","submitted_at":"2019-04-09T16:09:03Z","abstract_excerpt":"Let the coefficients $a_{ij}$ and $b_i$, $i,j \\leq d$, of the linear Fokker-Planck-Kolmogorov equation (FPK-eq.)\n  $$\\partial_t\\mu_t = \\partial_i\\partial_j(a_{ij}\\mu_t)-\\partial_i(b_i\\mu_t)$$ be Borel measurable, bounded and continuous in space. Assume that for every $s \\in [0,T]$ and every Borel probability measure $\\nu$ on $\\mathbb{R}^d$ there is at least one solution $\\mu = (\\mu_t)_{t \\in [s,T]}$ to the FPK-eq. such that $\\mu_s = \\nu$ and $t \\mapsto \\mu_t$ is continuous w.r.t. the topology of weak convergence of measures. We prove that in this situation, one can always select one solution $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04756","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":""},"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"}