{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:4F2Q37XEIX2SBXLCYLN2XGJYEQ","short_pith_number":"pith:4F2Q37XE","schema_version":"1.0","canonical_sha256":"e1750dfee445f520dd62c2dbab9938240daad6b912f7c5eb6d1b3c728350dd2b","source":{"kind":"arxiv","id":"0912.0782","version":2},"attestation_state":"computed","paper":{"title":"Gaussian and non-Gaussian processes of zero power variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francesco Russo (CERMICS, Frederi Viens, INRIA Rocquencourt, UMA)","submitted_at":"2009-12-04T07:48:43Z","abstract_excerpt":"This paper considers the class of stochastic processes $X$ which are Volterra convolutions of a martingale $M$. When $M$ is Brownian motion, $X$ is Gaussian, and the class includes fractional Brownian motion and other Gaussian processes with or without homogeneous increments. Let $m$ be an odd integer. Under some technical conditions on the quadratic variation of $M$, it is shown that the $m$-power variation exists and is zero when a quantity $\\delta^{2}(r) $ related to the variance of an increment of $M$ over a small interval of length $r$ satisfies $\\delta(r) = o(r^{1/(2m)}) $. In the case o"},"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":"0912.0782","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-04T07:48:43Z","cross_cats_sorted":[],"title_canon_sha256":"d7136433d5f494128d26dfe72a2280e14ec7e768bc62953e68fa942a1d7bfa2a","abstract_canon_sha256":"5f6279bddb52e0039a9058b9e062f2accd41507ba0eeac4be02e4d1b61342a81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:48.108770Z","signature_b64":"C9DlL5Pdz5nhCDfwZd75a44sZ1jjb721IaYrRzFIZD/hl1SL3yHygSQ8xJNjN3NmzsK4NbMy84l5b0xbVsFrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1750dfee445f520dd62c2dbab9938240daad6b912f7c5eb6d1b3c728350dd2b","last_reissued_at":"2026-05-18T03:54:48.108139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:48.108139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gaussian and non-Gaussian processes of zero power variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francesco Russo (CERMICS, Frederi Viens, INRIA Rocquencourt, UMA)","submitted_at":"2009-12-04T07:48:43Z","abstract_excerpt":"This paper considers the class of stochastic processes $X$ which are Volterra convolutions of a martingale $M$. When $M$ is Brownian motion, $X$ is Gaussian, and the class includes fractional Brownian motion and other Gaussian processes with or without homogeneous increments. Let $m$ be an odd integer. Under some technical conditions on the quadratic variation of $M$, it is shown that the $m$-power variation exists and is zero when a quantity $\\delta^{2}(r) $ related to the variance of an increment of $M$ over a small interval of length $r$ satisfies $\\delta(r) = o(r^{1/(2m)}) $. In the case o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0782","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0912.0782","created_at":"2026-05-18T03:54:48.108237+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.0782v2","created_at":"2026-05-18T03:54:48.108237+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0782","created_at":"2026-05-18T03:54:48.108237+00:00"},{"alias_kind":"pith_short_12","alias_value":"4F2Q37XEIX2S","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"4F2Q37XEIX2SBXLC","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"4F2Q37XE","created_at":"2026-05-18T12:25:58.837520+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4F2Q37XEIX2SBXLCYLN2XGJYEQ","json":"https://pith.science/pith/4F2Q37XEIX2SBXLCYLN2XGJYEQ.json","graph_json":"https://pith.science/api/pith-number/4F2Q37XEIX2SBXLCYLN2XGJYEQ/graph.json","events_json":"https://pith.science/api/pith-number/4F2Q37XEIX2SBXLCYLN2XGJYEQ/events.json","paper":"https://pith.science/paper/4F2Q37XE"},"agent_actions":{"view_html":"https://pith.science/pith/4F2Q37XEIX2SBXLCYLN2XGJYEQ","download_json":"https://pith.science/pith/4F2Q37XEIX2SBXLCYLN2XGJYEQ.json","view_paper":"https://pith.science/paper/4F2Q37XE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.0782&json=true","fetch_graph":"https://pith.science/api/pith-number/4F2Q37XEIX2SBXLCYLN2XGJYEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/4F2Q37XEIX2SBXLCYLN2XGJYEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4F2Q37XEIX2SBXLCYLN2XGJYEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4F2Q37XEIX2SBXLCYLN2XGJYEQ/action/storage_attestation","attest_author":"https://pith.science/pith/4F2Q37XEIX2SBXLCYLN2XGJYEQ/action/author_attestation","sign_citation":"https://pith.science/pith/4F2Q37XEIX2SBXLCYLN2XGJYEQ/action/citation_signature","submit_replication":"https://pith.science/pith/4F2Q37XEIX2SBXLCYLN2XGJYEQ/action/replication_record"}},"created_at":"2026-05-18T03:54:48.108237+00:00","updated_at":"2026-05-18T03:54:48.108237+00:00"}