The flow map of the Fokker-Planck equation does not provide optimal transport

被引：3
|
作者：
Lavenant, Hugo [1 ,2 ]
Santambrogio, Filippo [3 ]
机构：
[1] Bocconi Univ, Dept Decis Sci, I-20136 Milan, Italy
[2] Bocconi Univ, BIDSA, I-20136 Milan, Italy
[3] Univ Claude Bernard Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France
来源：
APPLIED MATHEMATICS LETTERS | 2022年 / 133卷
关键词：
Optimal transport; Fokker-Planck equation; Asymptotic behavior of solutions to  PDEs;
D O I：
10.1016/j.aml.2022.108225
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In Khrulkov and Oseledets (2022) the authors conjecture that, by integrating the flow of the ODE given by the Wasserstein velocity in a Fokker-Planck equation, one obtains an optimal transport map. On the other hand this result was thought to be false in Kim and Milman (2012) but no proof was provided. In this note we show that the result claimed by Khrulkov and Oseledets cannot hold. This strengthens a counterexample which was built in Tanana (2021). (c) 2022 Elsevier Ltd. All rights reserved.
引用
收藏
页数：7
相关论文
共 50 条
  • [21] PROPERTY OF FOKKER-PLANCK EQUATION
    COMBIS, P
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1978, 287 (06): : 473 - 476
  • [22] Quasicontinuum Fokker-Planck equation
    Alexander, Francis J.
    Rosenau, Philip
    PHYSICAL REVIEW E, 2010, 81 (04):
  • [23] Lattice Fokker-Planck equation
    Succi, S.
    Melchionna, S.
    Hansen, J. -P.
    INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2006, 17 (04): : 459 - 470
  • [24] COVARIANCE OF THE FOKKER-PLANCK EQUATION
    GARRIDO, L
    PHYSICA A, 1980, 100 (01): : 140 - 152
  • [25] On Quantum Fokker-Planck Equation
    Yano, Ryosuke
    JOURNAL OF STATISTICAL PHYSICS, 2015, 158 (01) : 231 - 247
  • [26] Fractional Fokker-Planck Equation
    Baumann, Gerd
    Stenger, Frank
    MATHEMATICS, 2017, 5 (01):
  • [27] FRACTIONAL FOKKER-PLANCK EQUATION
    Tristani, Isabelle
    COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2015, 13 (05) : 1243 - 1260
  • [28] INPAINTING WITH FOKKER-PLANCK EQUATION
    Ignat, Anca
    PROCEEDINGS OF THE ROMANIAN ACADEMY SERIES A-MATHEMATICS PHYSICS TECHNICAL SCIENCES INFORMATION SCIENCE, 2019, 20 (03): : 225 - 233
  • [29] ASPECTS OF FOKKER-PLANCK TRANSPORT
    CORNGOLD, N
    PROGRESS IN NUCLEAR ENERGY, 1981, 8 (2-3) : 163 - 170
  • [30] State Constrained Optimal Control via the Fokker-Planck Equation
    Rutquist, Per
    Wik, Torsten
    Breitholtz, Claes
    IFAC PAPERSONLINE, 2017, 50 (01): : 6303 - 6307
12345