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We prove that if \\a,\\b,\\g,\\th \\ge 0 are such that \\g + \\th < 1 and max[0,(\\a-\\b+\\th)] + \\g < 1/2, then the approximate solutions U_n (where n is the number of time steps) converge to the solution U in the Holder space C^\\g([0,T];E_\\a), both in L^p-means and almost surely, with rate 1/n^\\th."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0906.2129","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-06-11T15:11:53Z","cross_cats_sorted":["cs.NA","math.PR"],"title_canon_sha256":"9ed32ba5b663ace4cce0f098761e7ceb95bce790278f25eb87bd6526c733d483","abstract_canon_sha256":"7e7a57d478441ff6dd7e861d3e66cb66c5dbfa5f50db1818c8b9479851d8b855"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:27.050563Z","signature_b64":"uyKiG0yBEU2RtCHR2VtHpp9p4xINKLQP0xUQSn4B6WVT7fhe5sM89WLsJKMK+DdGje2IRGUm+DKcw+xbOITsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2bc9f55c4206f2cb8721c1d1ab6172f72aa376e7438f06f304d64f398b259be","last_reissued_at":"2026-06-03T23:06:27.049883Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:27.049883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence rates of the splitting scheme for parabolic linear stochastic Cauchy problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Jan van Neerven, Sonja Cox","submitted_at":"2009-06-11T15:11:53Z","abstract_excerpt":"We study the splitting scheme associated with the linear stochastic Cauchy problem dU(t) = AU(t) dt + dW(t), where A is the generator of an analytic C_0-semigroup S={S(t)} on a Banach space E and W={W(t)} is a Brownian motion with values in a fractional domain space E_\\b associated with A. 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