Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
A propagation of chaos result for Burgers' equation
Download PDF
Download PDF
  • Published: December 1986

A propagation of chaos result for Burgers' equation

  • A. S. Sznitman1 

Probability Theory and Related Fields volume 71, pages 581–613 (1986)Cite this article

  • 336 Accesses

  • 33 Citations

  • Metrics details

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Bibliography

  1. Barlow, M.T., Yor, M.: Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma and applications to local times. J. Functional Analysis49, 198–229 (1982)

    Google Scholar 

  2. Calderoni, P., Pulvirenti, M.: Propagation of chaos, for Burgers' equation. Ann. Inst. H. Poincaré, Sec. A (N.S.),39, 85–97 (1983)

    Google Scholar 

  3. Cole, J.D.: On a quasilinear parabolic equation occurring in aerodynamics. Quart. Appl. Math.,9, 225–236 (1951)

    Google Scholar 

  4. Dellacherie, C., Meyer, P.A.: Probabilités et Potentiels. Chap. V a VIII. Paris: Hermann 1980

    Google Scholar 

  5. Friedman, A.: Partial differential equations of parabolic type. London: Prentice Hall 1964

    Google Scholar 

  6. Gutkin, E., Kac, M.: Propagation of chaos and the Burgers' equation. SIAM J. Appl. Math.43, 971–980 (1983)

    Google Scholar 

  7. Harrison, J.M., Shepp, L.A.: On skew Brownian motion. Ann. Probability9, 309–313 (1981)

    Google Scholar 

  8. Hörmander, L.: The analysis of linear partial differential operators II. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  9. Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Amsterdam Kodansha, Tokyo: North-Holland 1981

    Google Scholar 

  10. Jacod, J.: Calcul stochastique et problèmes de martingales. Lecture Notes in Math. no 714. Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  11. Jeulin, T.: Semi-Martingales et grossissement d'une filtration. Lecture notes in Math.833. Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  12. Kac, M.: Foundation of kinetic theory. Proc. Third Berkeley Sympos. on Math. Statist. and Probab.3, 171–197. Univ. Calif. Press (1956)

    Google Scholar 

  13. Kotani, S., Osada, H.: Propagation of chaos for Burgers equation. J. Math. Soc. Japan37, 275–294 (1985)

    Google Scholar 

  14. Krylov, N.V.: Controlled diffusion processes. Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  15. McKean, H.P.: Propagation of chaos for a class of nonlinear parabolic equations. Lecture series in differential equations, Vol. 7, 41–57, Catholic University, Washington, D.C. (1967)

    Google Scholar 

  16. Nash, J.: Continuity of solutions of parabolic and elliptic equations. Am. J. Math.80, 931–954 (1958)

    Google Scholar 

  17. Osada, H.: Moment estimates for parabolic equations in the divergence form (preprint)

  18. Schwartz, L.: Théorie des distributions. Paris: Hermann 1978

    Google Scholar 

  19. Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton: University Press 1975

    Google Scholar 

  20. Sznitman, A.S.: Equations de type Boltzmann spatialement homogenes. Z. Wahrscheinlichkeitstheor. Verw. Geb.66, 559–592 (1984)

    Google Scholar 

  21. Sznitman, A.S., Varadhan, S.R.S.: A multidimensional process involving local time. Probab. Th. Rel. Fields71, 553–579 (1986)

    Google Scholar 

  22. Tanaka, H.: Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J.9, 163–177 (1979)

    Google Scholar 

  23. Tanaka, H.: Some probabilistic problems in the spatially homogeneous Boltzmann equation. In Proc. IFIP-ISI Conf. on Theory Appl. of Random Fields, Bangalore, Jan. 1982

  24. Yor, M.: Sur la continuité des temps locaux associés à certaines semi-martingales. Temps Locaux, Asterisque 52–53, 23–35. Soc. Math. France (1978)

  25. Zvonkin, A.K.: A transformation of the phase space of a diffusion process that removes the drift. Math. U.S.S.R., Sbornik22, 129–149 (1974)

    Google Scholar 

  26. Melnikov, A.V.: Stochastic equations and Krylov's estimates for semimartingales. Stochastics10, 81–102 (1983)

    Google Scholar 

  27. Oelschlager, K.: A law of large number for moderately interacting diffusion processes. Z. Wahrscheinlichkeitstheor. Verw. Geb.69, 279–322 (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Probabilités, associé C.N.R.S. no 224, Université Paris VI, 4, place Jussieu, F-75005, Paris, France

    A. S. Sznitman

Authors
  1. A. S. Sznitman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sznitman, A.S. A propagation of chaos result for Burgers' equation. Probab. Th. Rel. Fields 71, 581–613 (1986). https://doi.org/10.1007/BF00699042

Download citation

  • Received: 08 November 1984

  • Revised: 02 September 1985

  • Issue Date: December 1986

  • DOI: https://doi.org/10.1007/BF00699042

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Chaos Result
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature