{"paper":{"title":"Nonlinear parabolic characterizations of stochastic completeness at infinity on weighted graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Alberto G. Setti, Bobo Hua, Davide Bianchi, Rados{\\l}aw K. Wojciechowski","submitted_at":"2026-08-12T11:17:24Z","abstract_excerpt":"We prove a nonlinear parabolic characterization of stochastic completeness at infinity for weighted graphs. For the filtration equation \\[\n  (\\partial_t + \\Delta \\Phi)u =0 \\] where $\\Delta$ is the non-negative formal graph Laplacian and $\\Phi u =\\phi \\circ u$ with $\\phi \\colon \\R\\to\\R$ nonconstant, continuous and increasing, stochastic completeness at infinity is equivalent to uniqueness of bounded pointwise solutions for every bounded initial datum. For \\(\\Phi=\\id\\), this recovers the classical heat equation characterization of stochastic completeness at infinity, and of stochastic completene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11931","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/2608.11931/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"}