Mathematische Annalen

, Volume 287, Issue 1, pp 1–18 | Cite as

A stochastic characterization of harmonic morphisms

  • Laszlo Csink
  • P. J. Fitzsimmons
  • Bernt Øksendal


Harmonic Morphism Stochastic Characterization 
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. [BCD] Bernard, A., Campbell, E.A., Davie, A.M.: Brownian motion and generalized analytic and inner functions. Ann. Inst. Fourier29, 207–228 (1979)Google Scholar
  2. [BG] Blumenthal, R.M., Getoor, R.K.: Markov processes and potential theory. New York: Academic Press 1968Google Scholar
  3. [BGM] Blumenthal, R.M., Getoor, R.K., McKean, H.P. Jr.: Markov processes with identical hitting distributions. Ill. J. Math.6, 402–420 (1962);7, 540–542 (1963)Google Scholar
  4. [BH1] Bliedtner, J., Hansen, W.: Markov processes and harmonic spaces. Z. Wahrscheinlichkeitstheorie verw. Geb.42, 309–325 (1978)Google Scholar
  5. [BH2] Bliedtner, J., Hansen, W.: Potential Theory. Universitext, Berlin Heidelberg New York: Springer 1986Google Scholar
  6. [B] Boboc, N.: Asupra prelungiri aplicatiilor armonice. Ann. Univ. Craiova, Ser. Mat. Fiz. Chim.6, 31–36 (1978)Google Scholar
  7. [CC1] Constantinescu, C., Cornea, A.: Compactifications of harmonic spaces. Nagoya Math. J.25, 1–57 (1965)Google Scholar
  8. [CC2] Constantinescu, C., Cornea, A.: Potential Theory on Harmonic Spaces. Berlin Heidelberg New York: Springer 1972Google Scholar
  9. [CØ] Csink, L., Øksendal, B.: Stochastic harmonic morphisms: Functions mapping the paths of one diffusion into the paths of another. Ann. Inst. Fourier33, 219–240 (1983)Google Scholar
  10. [DM1] Dellacherie, C., Meyer, P.-A.: Probabilités et potentiel I (Chap. I à IV). Paris: Hermann 1975Google Scholar
  11. [DM2] Dellacherie, C., Meyer, P.-A.: Probabilités et potentiel VI (Chap. XII à XV) Paris: Hermann 1987Google Scholar
  12. [F1] Fuglede, B.: Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier28, 107–144 (1978)Google Scholar
  13. [F2] Fuglede, B.: Invariant characterizations of the fine topology in potential theory. Math. Ann.241, 187–192 (1979)Google Scholar
  14. [F3] Fuglede, B.: Harnack sets and openness of harmonic morphisms. Math. Ann.241, 181–186 (1979)Google Scholar
  15. [G] Getoor, R.K.: Markov processes: Ray processes and right processes. (Lect. Notes. Math., vol. 444) Berlin Heidelberg New York: Springer 1975Google Scholar
  16. [GS] Getoor, R.K., Sharpe, M.J.: Conformal martingales, Invent. Math.16, 271–308 (1972)Google Scholar
  17. [K] Kunita, H.: Absolute continuity of Markov processes and generators. Nagoya Math. J.36, 1–26 (1969)Google Scholar
  18. [L] Laine, I.: Covering properties of harmonicB1-mapping. Ann. Acad. Sci. Fenn., Ser. Al.1, 309–325 (1975)Google Scholar
  19. [McK] McKean, H.P. Jr.: Stochastic integrals. New York: Academic Press 1969Google Scholar
  20. [Ø1] Øksendal, B.: Finely harmonic morphisms, Brownian path preserving functions and conformal martingales. Invent. Math.75, 179–187 (1984)Google Scholar
  21. [Ø2] Øksendal, B.: Stochastic processes, infinitesimal generators and function theory. In Operators and function theory. S.C. Power (ed.) Dordrecht: Reidel 1985Google Scholar
  22. [Sh] Shih, C.T.: Markov processes whose hitting distributions are dominated by those of a given process. Trans. Am. Math. Soc.129, 157–179 (1967)Google Scholar
  23. [Si] Sibony, D.: Allure à la frontiére minimale d'une classe de transformation, Théorème de Doob généralisé, Ann. Inst. Fourier18, 91–120 (1968)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Laszlo Csink
    • 1
  • P. J. Fitzsimmons
    • 2
  • Bernt Øksendal
    • 3
  1. 1.Institute of Mathematics and Computer ScienceKando Kalman CollegeBudapestHungary
  2. 2.Department of Mathematics (C-012)University of California, San Diegola JollaUSA
  3. 3.Department of MathematicsUniversity of OsloOslo 3Norway

Personalised recommendations