{"paper":{"title":"Stochastic Calculus for Markov Processes Associated with Semi-Dirichlet Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chuan-Zhong Chen, Li Ma, Wei Sun","submitted_at":"2014-06-09T20:49:34Z","abstract_excerpt":"Let $(\\mathcal{E},D(\\mathcal{E}))$ be a quasi-regular semi-Dirichlet form and $(X_t)_{t\\geq0}$ be the associated Markov process. For $u\\in D(\\mathcal{E})_{loc}$, denote $A_t^{[u]}:=\\tilde{u}(X_{t})-\\tilde{u}(X_{0})$ and $F^{[u]}_t:=\\sum_{0<s\\leq t}(\\tilde u(X_{s})-\\tilde u(X_{s-}))1_{\\{|\\tilde u(X_{s})-\\tilde u(X_{s-})|>1\\}}$, where $\\tilde{u}$ is a quasi-continuous version of $u$. We show that there exist a unique locally square integrable martingale additive functional $Y^{[u]}$ and a unique continuous local additive functional $Z^{[u]}$ of zero quadratic variation such that $$A_t^{[u]}=Y_t^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2351","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"}