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• W3212532058 abstract "Let μ=(μ t ) t∈ℝ be any 1-parameter family of probability measures on ℝ. Its quantile process (G t ) t∈ℝ :]0,1[→ℝ ℝ , given by G t (α)=inf{x∈ℝ:μ t (]-∞,x])⩾α}, is not Markov in general. We modify it to build the Markov process we call “Markov-quantile”: there is a unique Markov process X with marginals μ t , being a limit for the finite dimensional topology of quantile processes where the past is made independent of the future at finitely many times (many non-Markovian limits exist in general). Strikingly, no regularity is required for the family μ. Moreover, if μ is increasing for the stochastic order, X has increasing trajectories. This is an analogue of a result of Kellerer dealing with the convex order. In a companion paper [8] it is also proved that if μ is absolutely continuous in the Wasserstein space 𝒫 2 (ℝ), X is solution of a Benamou–Brenier transport problem with marginals μ t , providing a Markov representation of the continuity equation, unique in the sense above." @default.
• W3212532058 created "2021-11-22" @default.
• W3212532058 creator A5031760673 @default.
• W3212532058 creator A5082237397 @default.
• W3212532058 date "2021-11-10" @default.
• W3212532058 modified "2023-10-01" @default.
• W3212532058 title "The Markov-quantile process attached to a family of marginals" @default.
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• W3212532058 doi "https://doi.org/10.5802/jep.177" @default.
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