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We modify it to build the Markov process we call \"Markov-quantile\".We first describe the discrete analogue: if ($\\mu$n)n$\\in$Z is a family of probability measures on R, a Markov process Y = (Yn)n$\\in$Z such that Law(Yn) = $\\mu$n is given by the data of its couplings from n to n + 1, i.e. Law((Yn, Yn+1)), and the process Y is the inhomogeneous Markov c"},"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":"1804.10514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-27T13:59:21Z","cross_cats_sorted":[],"title_canon_sha256":"a5df109c0e785dc63af2fa06eae38c999178e2c826c67f064f2f78729f25a8e3","abstract_canon_sha256":"67c8b6a4703ac25def93fc0e409c4f45099be11873aa1d56cd8e306c19f99103"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:20.546677Z","signature_b64":"iq+0X79856/FIY/JIxzgV+85yDKMKtEL4ZsyXOXHBfHvbGlSObFxsKeEpWNB3jgmxVcEWS/b2kENcrjp8sW3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"621aa6027f3efbe90367b6170532d695e0add45e5d1d2cda2c0ef2d7cfb2c2f2","last_reissued_at":"2026-05-18T00:17:20.546180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:20.546180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Markov-quantile process attached to a family of Marginals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Charles Boubel (IRMA), Nicolas Juillet (IRMA)","submitted_at":"2018-04-27T13:59:21Z","abstract_excerpt":"Let $\\mu$ = ($\\mu$t)t$\\in$R be any 1-parameter family of probability measures on R. Its quantile process (Gt)t$\\in$R : ]0, 1[ $\\rightarrow$ RR, given by Gt($\\alpha$) = inf{x $\\in$ R : $\\mu$t(]--$\\infty$, x]) > $\\alpha$}, is not Markov in general. We modify it to build the Markov process we call \"Markov-quantile\".We first describe the discrete analogue: if ($\\mu$n)n$\\in$Z is a family of probability measures on R, a Markov process Y = (Yn)n$\\in$Z such that Law(Yn) = $\\mu$n is given by the data of its couplings from n to n + 1, i.e. Law((Yn, Yn+1)), and the process Y is the inhomogeneous Markov c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10514","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":"1804.10514","created_at":"2026-05-18T00:17:20.546249+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.10514v1","created_at":"2026-05-18T00:17:20.546249+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10514","created_at":"2026-05-18T00:17:20.546249+00:00"},{"alias_kind":"pith_short_12","alias_value":"MINKMAT7H356","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"MINKMAT7H356SA3H","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"MINKMAT7","created_at":"2026-05-18T12:32:37.024351+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/MINKMAT7H356SA3HWYLQKMWWSX","json":"https://pith.science/pith/MINKMAT7H356SA3HWYLQKMWWSX.json","graph_json":"https://pith.science/api/pith-number/MINKMAT7H356SA3HWYLQKMWWSX/graph.json","events_json":"https://pith.science/api/pith-number/MINKMAT7H356SA3HWYLQKMWWSX/events.json","paper":"https://pith.science/paper/MINKMAT7"},"agent_actions":{"view_html":"https://pith.science/pith/MINKMAT7H356SA3HWYLQKMWWSX","download_json":"https://pith.science/pith/MINKMAT7H356SA3HWYLQKMWWSX.json","view_paper":"https://pith.science/paper/MINKMAT7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.10514&json=true","fetch_graph":"https://pith.science/api/pith-number/MINKMAT7H356SA3HWYLQKMWWSX/graph.json","fetch_events":"https://pith.science/api/pith-number/MINKMAT7H356SA3HWYLQKMWWSX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MINKMAT7H356SA3HWYLQKMWWSX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MINKMAT7H356SA3HWYLQKMWWSX/action/storage_attestation","attest_author":"https://pith.science/pith/MINKMAT7H356SA3HWYLQKMWWSX/action/author_attestation","sign_citation":"https://pith.science/pith/MINKMAT7H356SA3HWYLQKMWWSX/action/citation_signature","submit_replication":"https://pith.science/pith/MINKMAT7H356SA3HWYLQKMWWSX/action/replication_record"}},"created_at":"2026-05-18T00:17:20.546249+00:00","updated_at":"2026-05-18T00:17:20.546249+00:00"}