{"paper":{"title":"Approximative Theorem of Incomplete Riemann-Stieltjes Sum of Stochastic Integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.PR","authors_text":"Jingwei Liu","submitted_at":"2018-03-14T09:56:47Z","abstract_excerpt":"The approximative theorems of incomplete Riemann-Stieltjes sums of Ito stochastic integral, mean square integral and Stratonovich stochastic integral with respect to Brownian motion are investigated. Some sufficient conditions of incomplete Riemann-Stieltjes sums approaching stochastic integral are developed, which establish the alternative ways to converge stochastic integral. And, Two simulation examples of incomplete Riemann-Stieltjes sums about Ito stochastic integral and Stratonovich stochastic integral are given for demonstration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05182","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":""},"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"}