The European Physical Journal Special Topics

, Volume 226, Issue 3, pp 529–532 | Cite as

Invariants of Fokker-Planck equations

  • Sumiyoshi AbeEmail author
Regular Article
Part of the following topical collections:
  1. Nonlinearity, Nonequilibrium and Complexity: Questions and Perspectives in Statistical Physics


A weak invariant of a stochastic system is defined in such a way that its expectation value with respect to the distribution function as a solution of the associated Fokker-Planck equation is constant in time. A general formula is given for time evolution of the fluctuations of the invariant. An application to the problem of share price in finance is illustrated. It is shown how this theory makes it possible to reduce the growth rate of the fluctuations.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer-Verlag, Berlin, 1989)Google Scholar
  2. 2.
    K. Jacobs, Stochastic Processes for Physicists (Cambridge University Press, Cambridge, 2010)Google Scholar
  3. 3.
    S. Abe, Phys. Rev. A 94, 032116 (2016)ADSCrossRefGoogle Scholar
  4. 4.
    H.R. Lewis, Jr. , W.B. Riesenfeld, J. Math. Phys. 10, 1458 (1969)ADSCrossRefGoogle Scholar
  5. 5.
    C. Ou, S. Abe, EPL 113, 40009 (2016)ADSCrossRefGoogle Scholar
  6. 6.
    C. Ou, R.V. Chamberlin, S. Abe, Physica A 466, 450 (2017)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Physics Division, College of Information Science and Engineering, Huaqiao UniversityXiamen 361021, P.R.China
  2. 2.Department of Physical EngineeringMie UniversityMie 514-8507Japan
  3. 3.Institute of Physics, Kazan Federal UniversityKazan 420008Russia

Personalised recommendations