{"paper":{"title":"On Poisson equations with a potential in the whole space for \"ergodic\" generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Veretennikov","submitted_at":"2016-10-30T18:18:33Z","abstract_excerpt":"In earlier papers Poisson equation in the whole space was studied for so called ergodic generators $L$ corresponding to homogeneous Markov diffusions ($X_t, \\, t\\ge 0$) in $\\mathbb R^d$. Solving this equation is one of the main tools for diffusion approximation in the theory of stochastic averaging and homogenisation. Here a similar equation with a potential is considered, firstly because it is natural for PDEs, and secondly with a hope that it may be also useful for some extensions related to homogenization and averaging."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09687","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"}