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We prove continuous dependence of the compensated solutions X(t)-e^{tA}X_0 in the norms L^p(\\Omega;C^\\lambda([0,T];E)) assuming that the approximating operators A_n are uniformly sectorial and converge to A in the strong resolvent sense, and that the approximating "},"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":"1003.1876","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-09T14:08:14Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"00899f3616aae7f1fec3dd9d8426c4e3607d00bbd5da0f7b6de161f24215c1eb","abstract_canon_sha256":"87bdfad50ca95bec68af0d778d666f6912429ed2a499b4ca64310c014ad00628"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:44.618224Z","signature_b64":"3Ch4tm2LW+1J5QBE3Zi6sjp5U5wT3GimxGlzSKAhCzSKDZSiJ/CbQMoGvMoTBbnab7fzBlQzn16ieReMqKUUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae0de5a27c88946716c86e6b14994882c05abfe57533ba2ea21f2536f09a83fa","last_reissued_at":"2026-05-18T04:29:44.617795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:44.617795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating the coefficients in semilinear stochastic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Jan van Neerven, Markus Kunze","submitted_at":"2010-03-09T14:08:14Z","abstract_excerpt":"We investigate, in the setting of UMD Banach spaces E, the continuous dependence on the data A, F, G and X_0 of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form dX(t) = [AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical Brownian motion on a Hilbert space H. 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