{"paper":{"title":"Rate of convergence for numerical solutions to SFDEs with jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Chenggui Yuan, Jianhai Bao, Xuerong Mao","submitted_at":"2009-06-18T14:35:32Z","abstract_excerpt":"In this paper, we are interested in the numerical solutions of stochastic functional differential equations (SFDEs) with {\\it jumps}. Under the global Lipschitz condition, we show that the $p$th moment convergence of the Euler-Maruyama (EM) numerical solutions to SFDEs with jumps has order $1/p$ for any $p\\ge 2$. This is significantly different from the case of SFDEs without jumps where the order is 1/2 for any $p\\ge 2$. It is therefore best to use the mean-square convergence for SFDEs with jumps. Consequently, under the local Lipschitz condition, we reveal that the order of the mean-square co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3455","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/0906.3455/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"}