{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NMGOCOECV74JWH27S2VNX7BIZ5","short_pith_number":"pith:NMGOCOEC","schema_version":"1.0","canonical_sha256":"6b0ce13882aff89b1f5f96aadbfc28cf79e93ec26d0f05608c67ecb91fc7b86e","source":{"kind":"arxiv","id":"1601.08056","version":1},"attestation_state":"computed","paper":{"title":"Inversion, duality and Doob $h$-transforms for self-similar Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Larbi Alili, Lo\\\"ic Chaumont, Piotr Graczyk, Tomasz \\.Zak","submitted_at":"2016-01-29T11:12:15Z","abstract_excerpt":"We show that any $\\mathbb{R}^d\\setminus\\{0\\}$-valued self-similar Markov process $X$, with index $\\alpha>0$ can be represented as a path transformation of some Markov additive process (MAP) $(\\theta,\\xi)$ in $S_{d-1}\\times\\mathbb{R}$. This result extends the well known Lamperti transformation. Let us denote by $\\widehat{X}$ the self-similar Markov process which is obtained from the MAP $(\\theta,-\\xi)$ through this extended Lamperti transformation. Then we prove that $\\widehat{X}$ is in weak duality with $X$, with respect to the measure $\\pi(x/\\|x\\|)\\|x\\|^{\\alpha-d}dx$, if and only if $(\\theta,"},"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":"1601.08056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-29T11:12:15Z","cross_cats_sorted":[],"title_canon_sha256":"5756d13e44c9a3da26ab98082413def7f8588bd4487c5f69c4e8b24b5fe996aa","abstract_canon_sha256":"f760d3b96259e4cbb8ba3bf9ca75e0f820f591d634fe1bc45726677420be9376"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:41.051550Z","signature_b64":"t3QJbDcUyUhTPZlUV0qIVazz7pwL4k1IzTBYn9SbV+0M3ZdFT9NL8+81tXqJbYow0dI8UXSLfmL2ILPQ7t1rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b0ce13882aff89b1f5f96aadbfc28cf79e93ec26d0f05608c67ecb91fc7b86e","last_reissued_at":"2026-05-18T01:21:41.050942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:41.050942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inversion, duality and Doob $h$-transforms for self-similar Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Larbi Alili, Lo\\\"ic Chaumont, Piotr Graczyk, Tomasz \\.Zak","submitted_at":"2016-01-29T11:12:15Z","abstract_excerpt":"We show that any $\\mathbb{R}^d\\setminus\\{0\\}$-valued self-similar Markov process $X$, with index $\\alpha>0$ can be represented as a path transformation of some Markov additive process (MAP) $(\\theta,\\xi)$ in $S_{d-1}\\times\\mathbb{R}$. This result extends the well known Lamperti transformation. Let us denote by $\\widehat{X}$ the self-similar Markov process which is obtained from the MAP $(\\theta,-\\xi)$ through this extended Lamperti transformation. Then we prove that $\\widehat{X}$ is in weak duality with $X$, with respect to the measure $\\pi(x/\\|x\\|)\\|x\\|^{\\alpha-d}dx$, if and only if $(\\theta,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08056","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":"1601.08056","created_at":"2026-05-18T01:21:41.051030+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.08056v1","created_at":"2026-05-18T01:21:41.051030+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08056","created_at":"2026-05-18T01:21:41.051030+00:00"},{"alias_kind":"pith_short_12","alias_value":"NMGOCOECV74J","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NMGOCOECV74JWH27","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NMGOCOEC","created_at":"2026-05-18T12:30:32.724797+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/NMGOCOECV74JWH27S2VNX7BIZ5","json":"https://pith.science/pith/NMGOCOECV74JWH27S2VNX7BIZ5.json","graph_json":"https://pith.science/api/pith-number/NMGOCOECV74JWH27S2VNX7BIZ5/graph.json","events_json":"https://pith.science/api/pith-number/NMGOCOECV74JWH27S2VNX7BIZ5/events.json","paper":"https://pith.science/paper/NMGOCOEC"},"agent_actions":{"view_html":"https://pith.science/pith/NMGOCOECV74JWH27S2VNX7BIZ5","download_json":"https://pith.science/pith/NMGOCOECV74JWH27S2VNX7BIZ5.json","view_paper":"https://pith.science/paper/NMGOCOEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.08056&json=true","fetch_graph":"https://pith.science/api/pith-number/NMGOCOECV74JWH27S2VNX7BIZ5/graph.json","fetch_events":"https://pith.science/api/pith-number/NMGOCOECV74JWH27S2VNX7BIZ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NMGOCOECV74JWH27S2VNX7BIZ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NMGOCOECV74JWH27S2VNX7BIZ5/action/storage_attestation","attest_author":"https://pith.science/pith/NMGOCOECV74JWH27S2VNX7BIZ5/action/author_attestation","sign_citation":"https://pith.science/pith/NMGOCOECV74JWH27S2VNX7BIZ5/action/citation_signature","submit_replication":"https://pith.science/pith/NMGOCOECV74JWH27S2VNX7BIZ5/action/replication_record"}},"created_at":"2026-05-18T01:21:41.051030+00:00","updated_at":"2026-05-18T01:21:41.051030+00:00"}