{"paper":{"title":"Infinite-dimensional nonlinear stationary Fokker-Planck-Kolmogorov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Michael R\\\"ockner, Stanislav V. Shaposhnikov, Vladimir I. Bogachev","submitted_at":"2025-11-28T10:32:32Z","abstract_excerpt":"We prove existence of a probability solution to the nonlinear stationary Fokker-Planck-Kolmogorov equation on an infinite dimensional space with a centered Gaussian measure $\\gamma$ with a unit diffusion operator and a drift of the form $-x+v(p,x)$, where $v$ is a bounded mapping with values in the Cameron-Martin space $H$ of $\\gamma$ and $v$ is defined on the space $E\\times X$, where is $E$ is the subset of $L^2(\\gamma)$ consisting of probability densities. The equation has the form $L_{b(p,\\bullet)} ^*(p\\cdot \\gamma)=0$ with $L_{b(p,\\bullet)}\\varphi =\\Delta_H \\varphi + (b(p,\\bullet) , D_{_H}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.23058","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/2511.23058/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"}