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We show that if $S_n$ converges in finite dimensional distributions to a c\\`{a}dl\\`{a}g process, then $S_n+y_n$ converges a.s. pathwise uniformly over $[0,1]$, for some $y_n\\in D([0,1];E)$. This result extends the It\\^{o}-Nisio theorem to the space $D([0,1];E)$, which is surprisingly lacking in the literature even for $E=R$. The main difficulties of dealing with $D([0,1];E)$ in this context are its nonseparability unde"},"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":"1111.1682","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-07T19:13:40Z","cross_cats_sorted":[],"title_canon_sha256":"18cc3c137e3e44ab640447ab74e6e2dfccc7cf8f49ee7135d7274a1332eef3d3","abstract_canon_sha256":"93eded9f0559b1246f50fb8f21cadee363ee2ba74c9c636de65e091618f7231b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:24.417240Z","signature_b64":"gJBKKjUq/WZG99rs03Lgqx1ikXHkpdJFJeoz9c6sU1hER5O6kF+oQkywFhcmR6p1S075d1va3TVraII2SGGPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c79937971cb064fa388b81bf21d7b8cd83bf42ab053218f3c26a39a6c01dee16","last_reissued_at":"2026-05-18T03:04:24.416788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:24.416788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the uniform convergence of random series in Skorohod space and representations of c\\`{a}dl\\`{a}g infinitely divisible processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas Basse-O'Connor, Jan Rosi\\'nski","submitted_at":"2011-11-07T19:13:40Z","abstract_excerpt":"Let $X_n$ be independent random elements in the Skorohod space $D([0,1];E)$ of c\\`{a}dl\\`{a}g functions taking values in a separable Banach space $E$. 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