{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:YZ27B2WPLU3L6MAS2NOSEGYDEQ","short_pith_number":"pith:YZ27B2WP","schema_version":"1.0","canonical_sha256":"c675f0eacf5d36bf3012d35d221b0324181f7d4b3b86ed08afbbf16903fac445","source":{"kind":"arxiv","id":"1605.00880","version":2},"attestation_state":"computed","paper":{"title":"Rate of convergence to equilibrium of fractional driven stochastic differential equations with rough multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aur\\'elien Deya, Fabien Panloup, Samy Tindel","submitted_at":"2016-05-03T12:59:32Z","abstract_excerpt":"We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\\in (1/3,1)$ and multiplicative noise component $\\sigma$. When $\\sigma$ is constant and for every $H\\in (0,1)$, it was proved in [19] that, under some mean-reverting assumptions, such a process converges to its equilibrium at a rate of order $t^{-\\alpha}$ where $\\alpha \\in (0,1)$ (depending on $H$). In [11], this result has been extended to the multiplicative case when $H\\textgreater{}1/2$. In this paper, we obtain these "},"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":"1605.00880","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-03T12:59:32Z","cross_cats_sorted":[],"title_canon_sha256":"624de05ef567d3ff7b5ae5f050b50f8c145563f6682751e048edc80e19b2cce6","abstract_canon_sha256":"544834170d943e3e1e277c0bc0edf04a1668f30e3c4636475b25b0473461372c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:19.107157Z","signature_b64":"XprlbGTx/gMOuYwmzSzskpGMNvnv5iFSS0qxilwbFZIALYpCyZrTZgCwtGp3hO7J9g/1bgiHocURC7wCgc6ACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c675f0eacf5d36bf3012d35d221b0324181f7d4b3b86ed08afbbf16903fac445","last_reissued_at":"2026-05-18T01:03:19.106765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:19.106765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rate of convergence to equilibrium of fractional driven stochastic differential equations with rough multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aur\\'elien Deya, Fabien Panloup, Samy Tindel","submitted_at":"2016-05-03T12:59:32Z","abstract_excerpt":"We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\\in (1/3,1)$ and multiplicative noise component $\\sigma$. When $\\sigma$ is constant and for every $H\\in (0,1)$, it was proved in [19] that, under some mean-reverting assumptions, such a process converges to its equilibrium at a rate of order $t^{-\\alpha}$ where $\\alpha \\in (0,1)$ (depending on $H$). In [11], this result has been extended to the multiplicative case when $H\\textgreater{}1/2$. In this paper, we obtain these "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00880","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":"1605.00880","created_at":"2026-05-18T01:03:19.106816+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.00880v2","created_at":"2026-05-18T01:03:19.106816+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00880","created_at":"2026-05-18T01:03:19.106816+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZ27B2WPLU3L","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZ27B2WPLU3L6MAS","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZ27B2WP","created_at":"2026-05-18T12:30:53.716459+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/YZ27B2WPLU3L6MAS2NOSEGYDEQ","json":"https://pith.science/pith/YZ27B2WPLU3L6MAS2NOSEGYDEQ.json","graph_json":"https://pith.science/api/pith-number/YZ27B2WPLU3L6MAS2NOSEGYDEQ/graph.json","events_json":"https://pith.science/api/pith-number/YZ27B2WPLU3L6MAS2NOSEGYDEQ/events.json","paper":"https://pith.science/paper/YZ27B2WP"},"agent_actions":{"view_html":"https://pith.science/pith/YZ27B2WPLU3L6MAS2NOSEGYDEQ","download_json":"https://pith.science/pith/YZ27B2WPLU3L6MAS2NOSEGYDEQ.json","view_paper":"https://pith.science/paper/YZ27B2WP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.00880&json=true","fetch_graph":"https://pith.science/api/pith-number/YZ27B2WPLU3L6MAS2NOSEGYDEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/YZ27B2WPLU3L6MAS2NOSEGYDEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZ27B2WPLU3L6MAS2NOSEGYDEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZ27B2WPLU3L6MAS2NOSEGYDEQ/action/storage_attestation","attest_author":"https://pith.science/pith/YZ27B2WPLU3L6MAS2NOSEGYDEQ/action/author_attestation","sign_citation":"https://pith.science/pith/YZ27B2WPLU3L6MAS2NOSEGYDEQ/action/citation_signature","submit_replication":"https://pith.science/pith/YZ27B2WPLU3L6MAS2NOSEGYDEQ/action/replication_record"}},"created_at":"2026-05-18T01:03:19.106816+00:00","updated_at":"2026-05-18T01:03:19.106816+00:00"}