{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:V5UEC3A5BGKFG53BGDRQB52KWR","short_pith_number":"pith:V5UEC3A5","schema_version":"1.0","canonical_sha256":"af68416c1d099453776130e300f74ab45b76634b581a1c47894f2ab289fd9322","source":{"kind":"arxiv","id":"1803.02625","version":1},"attestation_state":"computed","paper":{"title":"A new Multifractional Process with Random Exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antoine Ayache, C\\'eline Esser, Julien Hamonier","submitted_at":"2018-03-07T12:53:15Z","abstract_excerpt":"A first type of Multifractional Process with Random Exponent (MPRE) was constructed several years ago in (Ayache, Taqqu, 2005) by replacing in a wavelet series representation of Fractional Brownian Motion (FBM) the Hurst parameter by a random variable depending on the time variable. In the present article, we propose another approach for constructing another type of MPRE. It consists in substituting to the Hurst parameter, in a stochastic integral representation of the high-frequency part of FBM, a random variable depending on the integration variable. The MPRE obtained in this way offers, amo"},"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":"1803.02625","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-07T12:53:15Z","cross_cats_sorted":[],"title_canon_sha256":"e931a66969e2ada1f20c3d8490a7bc9954af10c1a205d946c15d93a84c82620a","abstract_canon_sha256":"8ecda57b7df585faacba3444aae1791d54c28ac747180d06fead01b835cdf5cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:49.657475Z","signature_b64":"G807B/izkqT7xBE0I92h2sqse7HjHGRUkTZTYLgbhiKAAS+D8exvDC1C7QpInvABA5cmK8hsvecBFP3B+BI3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af68416c1d099453776130e300f74ab45b76634b581a1c47894f2ab289fd9322","last_reissued_at":"2026-05-18T00:21:49.656753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:49.656753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new Multifractional Process with Random Exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antoine Ayache, C\\'eline Esser, Julien Hamonier","submitted_at":"2018-03-07T12:53:15Z","abstract_excerpt":"A first type of Multifractional Process with Random Exponent (MPRE) was constructed several years ago in (Ayache, Taqqu, 2005) by replacing in a wavelet series representation of Fractional Brownian Motion (FBM) the Hurst parameter by a random variable depending on the time variable. In the present article, we propose another approach for constructing another type of MPRE. It consists in substituting to the Hurst parameter, in a stochastic integral representation of the high-frequency part of FBM, a random variable depending on the integration variable. The MPRE obtained in this way offers, amo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02625","kind":"arxiv","version":1},"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":"1803.02625","created_at":"2026-05-18T00:21:49.656871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.02625v1","created_at":"2026-05-18T00:21:49.656871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02625","created_at":"2026-05-18T00:21:49.656871+00:00"},{"alias_kind":"pith_short_12","alias_value":"V5UEC3A5BGKF","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"V5UEC3A5BGKFG53B","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"V5UEC3A5","created_at":"2026-05-18T12:32:59.047623+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/V5UEC3A5BGKFG53BGDRQB52KWR","json":"https://pith.science/pith/V5UEC3A5BGKFG53BGDRQB52KWR.json","graph_json":"https://pith.science/api/pith-number/V5UEC3A5BGKFG53BGDRQB52KWR/graph.json","events_json":"https://pith.science/api/pith-number/V5UEC3A5BGKFG53BGDRQB52KWR/events.json","paper":"https://pith.science/paper/V5UEC3A5"},"agent_actions":{"view_html":"https://pith.science/pith/V5UEC3A5BGKFG53BGDRQB52KWR","download_json":"https://pith.science/pith/V5UEC3A5BGKFG53BGDRQB52KWR.json","view_paper":"https://pith.science/paper/V5UEC3A5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.02625&json=true","fetch_graph":"https://pith.science/api/pith-number/V5UEC3A5BGKFG53BGDRQB52KWR/graph.json","fetch_events":"https://pith.science/api/pith-number/V5UEC3A5BGKFG53BGDRQB52KWR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V5UEC3A5BGKFG53BGDRQB52KWR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V5UEC3A5BGKFG53BGDRQB52KWR/action/storage_attestation","attest_author":"https://pith.science/pith/V5UEC3A5BGKFG53BGDRQB52KWR/action/author_attestation","sign_citation":"https://pith.science/pith/V5UEC3A5BGKFG53BGDRQB52KWR/action/citation_signature","submit_replication":"https://pith.science/pith/V5UEC3A5BGKFG53BGDRQB52KWR/action/replication_record"}},"created_at":"2026-05-18T00:21:49.656871+00:00","updated_at":"2026-05-18T00:21:49.656871+00:00"}