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We consider extensions of this result to non Gaussian infinitely divisible processes. First we show that the class of infinitely divisible semimartingales is so large that the natural analog of Stricker's theorem fails to hold. Then, as the main result, we prove that an infinitely divisible semimartingale relative to the filtration generat"},"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":"1404.7598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-30T06:08:19Z","cross_cats_sorted":[],"title_canon_sha256":"8fba1cb48926bb50642eb7a5529b4818d35a79c3ddd4bf89bef899f336ae080e","abstract_canon_sha256":"5255b45aa87987b69186aa3335cae6c710122e31a6d852f6da926afc8dfd21b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:30.011470Z","signature_b64":"vHprV2auYAxsk4/W2FzI4FXIS7mDiAVhAq16dfCz5Bk1DJ6Z7gRWd9P6N87MrG4eIh6/In6h7+tPQrH4+i/xDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"572bd0958b77dcef2a8260411da37a15631867694822ba83eed2e00c1f65448a","last_reissued_at":"2026-05-18T02:31:30.011084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:30.011084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On infinitely divisible semimartingales","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":"2014-04-30T06:08:19Z","abstract_excerpt":"Stricker's theorem states that a Gaussian process is a semimartingale in its natural filtration if and only if it is the sum of an independent increment Gaussian process and a Gaussian process of finite variation, see [1983, Z. 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