{"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"}