Some Properties of Path Measures

  • Christian Léonard
Part of the Lecture Notes in Mathematics book series (LNM, volume 2123)


We call any measure on a path space, a path measure. Some notions about path measures which appear naturally when solving the Schrödinger problem are presented and worked out in detail.


Unbounded measure Conditional expectation Relative entropy Stochastic processes Schrödinger problem 

AMS classification (2010):

28A50 60J25 


  1. 1.
    R.M. Dudley, Real Analysis and Probability. Cambridge Studies in Advanced Mathematics, vol. 74 (Cambridge University Press, Cambridge, 2002). Revised reprint of the 1989 originalGoogle Scholar
  2. 2.
    H. Föllmer, Random fields and diffusion processes, in École d’été de Probabilités de Saint-Flour XV-XVII-1985-87. Lecture Notes in Mathematics, vol. 1362 (Springer, Berlin, 1988)Google Scholar
  3. 3.
    N. Gozlan, C. Léonard, Transport inequalities: a survey. Markov Process. Relat. Fields 16, 635–736 (2010)zbMATHGoogle Scholar
  4. 4.
    F. Kelly, Reversibility and Stochastic Networks (Cambridge University Press, Cambridge, 2011)zbMATHGoogle Scholar
  5. 5.
    C. Léonard, A survey of the Schrödinger problem and some of its connections with optimal transport. Discrete Contin. Dyn. Syst. A 34(4), 1533–1574 (2014)CrossRefzbMATHGoogle Scholar
  6. 6.
    W. Rudin, Real and Complex Analysis (McGraw-Hill, New York, 1987)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Modal-X, Université Paris OuestNanterreFrance

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