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We prove that the approximation of the derivative of self-intersection local time, defined as \\begin{align*} \\alpha_{\\varepsilon} &= \\int_{0}^{T}\\int_{0}^{t}p'_{\\varepsilon}(B_{t}-B_{s})\\text{d}s\\text{d}t, \\end{align*} where $p_\\varepsilon(x)$ is the heat kernel, satisfies a central limit theorem when renormalized by $\\varepsilon^{\\frac{3}{2}-\\frac{1}{H}}$. We prove as well that for $q\\geq2$, the $q$-th chaotic component of $\\alpha_{\\varepsilon}$ converges in $L^{2}$ when $\\frac{2}{3}<H<\\frac{3}{4}"},"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":"1512.07219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-22T19:50:28Z","cross_cats_sorted":[],"title_canon_sha256":"b8e406e2d4c688647d7e61a6874508a0c544bdb868839cfbc9393645f64eb39d","abstract_canon_sha256":"c94394cd88e97bab7fe9debffb64688dd3967abe9810089e599c3dd6860f6927"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:52.598910Z","signature_b64":"1Lj4rdPI2OSGaUKfVxC4bDdvj3spNIlJEnmmmLbJOu+sbjyffxvMRS/7DmX7VBLIg2QmV2WVGl9+7hMrk28iBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7ad9fd473d4fbcf881aabe2b5c0bb9ecdf065f0fe387ae86fb67f251732f9f9","last_reissued_at":"2026-05-18T01:23:52.598352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:52.598352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic properties of the derivative of self-intersection local time of fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arturo Jaramillo, David Nualart","submitted_at":"2015-12-22T19:50:28Z","abstract_excerpt":"Let $\\{B_{t}\\}_{t\\geq0}$ be a fractional Brownian motion with Hurst parameter $\\frac{2}{3}<H<1$. We prove that the approximation of the derivative of self-intersection local time, defined as \\begin{align*} \\alpha_{\\varepsilon} &= \\int_{0}^{T}\\int_{0}^{t}p'_{\\varepsilon}(B_{t}-B_{s})\\text{d}s\\text{d}t, \\end{align*} where $p_\\varepsilon(x)$ is the heat kernel, satisfies a central limit theorem when renormalized by $\\varepsilon^{\\frac{3}{2}-\\frac{1}{H}}$. We prove as well that for $q\\geq2$, the $q$-th chaotic component of $\\alpha_{\\varepsilon}$ converges in $L^{2}$ when $\\frac{2}{3}<H<\\frac{3}{4}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07219","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":"1512.07219","created_at":"2026-05-18T01:23:52.598440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.07219v1","created_at":"2026-05-18T01:23:52.598440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07219","created_at":"2026-05-18T01:23:52.598440+00:00"},{"alias_kind":"pith_short_12","alias_value":"46WZ7VDT2T54","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"46WZ7VDT2T547CA2","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"46WZ7VDT","created_at":"2026-05-18T12:29:05.191682+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/46WZ7VDT2T547CA2VPRLLQF3T3","json":"https://pith.science/pith/46WZ7VDT2T547CA2VPRLLQF3T3.json","graph_json":"https://pith.science/api/pith-number/46WZ7VDT2T547CA2VPRLLQF3T3/graph.json","events_json":"https://pith.science/api/pith-number/46WZ7VDT2T547CA2VPRLLQF3T3/events.json","paper":"https://pith.science/paper/46WZ7VDT"},"agent_actions":{"view_html":"https://pith.science/pith/46WZ7VDT2T547CA2VPRLLQF3T3","download_json":"https://pith.science/pith/46WZ7VDT2T547CA2VPRLLQF3T3.json","view_paper":"https://pith.science/paper/46WZ7VDT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.07219&json=true","fetch_graph":"https://pith.science/api/pith-number/46WZ7VDT2T547CA2VPRLLQF3T3/graph.json","fetch_events":"https://pith.science/api/pith-number/46WZ7VDT2T547CA2VPRLLQF3T3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/46WZ7VDT2T547CA2VPRLLQF3T3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/46WZ7VDT2T547CA2VPRLLQF3T3/action/storage_attestation","attest_author":"https://pith.science/pith/46WZ7VDT2T547CA2VPRLLQF3T3/action/author_attestation","sign_citation":"https://pith.science/pith/46WZ7VDT2T547CA2VPRLLQF3T3/action/citation_signature","submit_replication":"https://pith.science/pith/46WZ7VDT2T547CA2VPRLLQF3T3/action/replication_record"}},"created_at":"2026-05-18T01:23:52.598440+00:00","updated_at":"2026-05-18T01:23:52.598440+00:00"}