Journal of Mathematical Sciences

, Volume 207, Issue 2, pp 147–165 | Cite as

Uniqueness Problems for Degenerate Fokker–Planck–Kolmogorov Equations

  • V. I. BogachevEmail author
  • M. Röckner
  • S. V. Shaposhnikov

We study the uniqueness of solutions to the Cauchy problem for the Fokker–Planck–Kolmogorov equation with a singular diffusion matrix in the class of probability measures. A survey of known result and methods is given. In addition, we obtain new sufficient conditions for the uniqueness in the case of unbounded coefficients and a partially singular diffusion matrix and also in the case where the diffusion matrix is a squared Lipschitzian matrix.


Probability Measure Cauchy Problem Lebesgue Measure Borel Measure Planck Equation 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. I. Bogachev
    • 1
    • 2
    Email author
  • M. Röckner
    • 3
  • S. V. Shaposhnikov
    • 1
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.St. Tikhon’s Orthodox Humanitarian UniversityMoscowRussia
  3. 3.Universität BielefeldBielefeldGermany

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