{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZRAJGTAPDOSEMXTCUEBKXX4EFZ","short_pith_number":"pith:ZRAJGTAP","schema_version":"1.0","canonical_sha256":"cc40934c0f1ba4465e62a102abdf842e4622c911e2b2b608e1ff9a89b42832c7","source":{"kind":"arxiv","id":"1506.06966","version":6},"attestation_state":"computed","paper":{"title":"Rates in the Central Limit Theorem and diffusion approximation via Stein's Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Thomas Bonis","submitted_at":"2015-06-23T12:15:03Z","abstract_excerpt":"We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\\nu$ and $\\mu$ supported on $\\mathbb{R}^d$ such that $\\mu$ is the reversible measure of a diffusion process. In order to apply our result, we only require to have access to a stochastic process $(X_t)_{t \\geq 0}$ such that $X_t$ is drawn from $\\nu$ for any $t > 0$. We then show that, whenever $\\mu$ is the Gaussian measure $\\gamma$, one can use a slightly different approach to bound the Wasserstein distances of order $p \\geq 1$ between $\\nu$ and $\\gamma$ under an additional excha"},"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":"1506.06966","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-23T12:15:03Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b4f0ca335404895cf51f390352358c77b990637ee8bc8f9f4151a3cb8ec5db56","abstract_canon_sha256":"1aca8eb8060302c46a47c321785073ffbf499e8b2a0d9c0b9cc4edccb142c5ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:41.052172Z","signature_b64":"FP2DkdoC+laiXnNeLs8m8RF0urrNz/M3v6zek0xHBmoT90ebc5+XVF66QT6LuZAEBTuo3FeQTheR/z5yyUZGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc40934c0f1ba4465e62a102abdf842e4622c911e2b2b608e1ff9a89b42832c7","last_reissued_at":"2026-05-18T00:12:41.051629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:41.051629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rates in the Central Limit Theorem and diffusion approximation via Stein's Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Thomas Bonis","submitted_at":"2015-06-23T12:15:03Z","abstract_excerpt":"We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\\nu$ and $\\mu$ supported on $\\mathbb{R}^d$ such that $\\mu$ is the reversible measure of a diffusion process. In order to apply our result, we only require to have access to a stochastic process $(X_t)_{t \\geq 0}$ such that $X_t$ is drawn from $\\nu$ for any $t > 0$. We then show that, whenever $\\mu$ is the Gaussian measure $\\gamma$, one can use a slightly different approach to bound the Wasserstein distances of order $p \\geq 1$ between $\\nu$ and $\\gamma$ under an additional excha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06966","kind":"arxiv","version":6},"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":"1506.06966","created_at":"2026-05-18T00:12:41.051705+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.06966v6","created_at":"2026-05-18T00:12:41.051705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06966","created_at":"2026-05-18T00:12:41.051705+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZRAJGTAPDOSE","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZRAJGTAPDOSEMXTC","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZRAJGTAP","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.03833","citing_title":"Computable Bounds for Strong Approximations with Applications","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZRAJGTAPDOSEMXTCUEBKXX4EFZ","json":"https://pith.science/pith/ZRAJGTAPDOSEMXTCUEBKXX4EFZ.json","graph_json":"https://pith.science/api/pith-number/ZRAJGTAPDOSEMXTCUEBKXX4EFZ/graph.json","events_json":"https://pith.science/api/pith-number/ZRAJGTAPDOSEMXTCUEBKXX4EFZ/events.json","paper":"https://pith.science/paper/ZRAJGTAP"},"agent_actions":{"view_html":"https://pith.science/pith/ZRAJGTAPDOSEMXTCUEBKXX4EFZ","download_json":"https://pith.science/pith/ZRAJGTAPDOSEMXTCUEBKXX4EFZ.json","view_paper":"https://pith.science/paper/ZRAJGTAP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.06966&json=true","fetch_graph":"https://pith.science/api/pith-number/ZRAJGTAPDOSEMXTCUEBKXX4EFZ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZRAJGTAPDOSEMXTCUEBKXX4EFZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZRAJGTAPDOSEMXTCUEBKXX4EFZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZRAJGTAPDOSEMXTCUEBKXX4EFZ/action/storage_attestation","attest_author":"https://pith.science/pith/ZRAJGTAPDOSEMXTCUEBKXX4EFZ/action/author_attestation","sign_citation":"https://pith.science/pith/ZRAJGTAPDOSEMXTCUEBKXX4EFZ/action/citation_signature","submit_replication":"https://pith.science/pith/ZRAJGTAPDOSEMXTCUEBKXX4EFZ/action/replication_record"}},"created_at":"2026-05-18T00:12:41.051705+00:00","updated_at":"2026-05-18T00:12:41.051705+00:00"}