Summary
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.
Article PDF
Similar content being viewed by others
References
Funaki, T.: The diffusion approximation of the Boltzmann equation of Maxwellian molecules. Publ. RIMS Kyoto Univ. 19, 841–886 (1983)
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.
Hille, E.: Topics in classical analysis. In: Lectures on Modern Mathematics III, pp. 1–57. New York: John Wiley 1965
Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Amsterdam-Tokyo: North-Holland/Kodansha 1981
Kuratowski, K., Ryll-Nardzewski, C.: A general theorem on selectors. Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron. Phys. 13, 397–403 (1965)
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. 1967
Stroock, D.W., Varadhan, S.R.S.: Multidimensional diffusion processes. Berlin-Heidelberg-New York: Springer 1979
Echeverria, P.: A criterion for invariant measures of Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 61, 1–16 (1982)
Author information
Authors and Affiliations
Additional information
Research partially supported by the Air Force Office of Scientific Research Contract No. F4962082C0009
Rights and permissions
About this article
Cite this article
Funaki, T. A certain class of diffusion processes associated with nonlinear parabolic equations. Z. Wahrscheinlichkeitstheorie verw Gebiete 67, 331–348 (1984). https://doi.org/10.1007/BF00535008
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00535008