{"paper":{"title":"Explosion by Killing and Maximum Principle in Symmetric Markov Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Masayoshi Takeda","submitted_at":"2024-06-23T00:36:22Z","abstract_excerpt":"Keller and Lenz \\cite{KL} define a concept of {\\it stochastic completeness at infinity} (SCI) for a regular symmetric Dirichlet form $(\\cE,\\cF)$. We show that (SCI) can be characterized probabilistically by using the predictable part $\\zeta^p$ of the life time $\\zeta$ of the symmetric Markov process $X=({\\bf P}_x,X_t)$ generated by $(\\cE,\\cF)$, that is, (SCI) is equivalent to $\\bfP_x(\\zeta=\\zeta^p<\\infty)=0$. We define a concept, {\\it explosion by killing} (EK), by $\\bfP_x(\\zeta=\\zeta^i<\\infty)=1$. Here $\\zeta^i$ is the totally inaccessible part of $\\zeta$. We see that (EK) is equivalent to (S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.15974","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/2406.15974/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"}