A certain class of diffusion processes associated with nonlinear parabolic equations

  • Tadahisa Funaki


We introduce a martingale problem to associate diffusion processes with a kind of nonlinear parabolic equation. Then we show the existence and uniqueness theorems for solutions to the martingale problem.


Probability Measure Stochastic Differential Equation Uniqueness Theorem Markov Property Nonlinear Parabolic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Funaki, T.: The diffusion approximation of the Boltzmann equation of Maxwellian molecules. Publ. RIMS Kyoto Univ. 19, 841–886 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Funaki, T.: The diffusion approximation of the spatially homogeneous Boltzmann equation. Technical Report #52, Center for Stochastic Processes, Dept. of Statistics, Univ. of North Carolina at Chapel Hill (1983), to appear in Duke Math. J.Google Scholar
  3. 3.
    Hille, E.: Topics in classical analysis. In: Lectures on Modern Mathematics III, pp. 1–57. New York: John Wiley 1965Google Scholar
  4. 4.
    Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Amsterdam-Tokyo: North-Holland/Kodansha 1981zbMATHGoogle Scholar
  5. 5.
    Kuratowski, K., Ryll-Nardzewski, C.: A general theorem on selectors. Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron. Phys. 13, 397–403 (1965)MathSciNetzbMATHGoogle Scholar
  6. 6.
    McKean, H.P.: Propagation of chaos for a class of non-linear parabolic equations. In: Lecture Series in Differential Equations, session 7, pp. 177–194. Catholic Univ. 1967Google Scholar
  7. 7.
    Stroock, D.W., Varadhan, S.R.S.: Multidimensional diffusion processes. Berlin-Heidelberg-New York: Springer 1979zbMATHGoogle Scholar
  8. 8.
    Echeverria, P.: A criterion for invariant measures of Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 61, 1–16 (1982)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Tadahisa Funaki
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceNagoya UniversityNagoyaJapan

Personalised recommendations