Skip to main content
Log in

A stochastic characterization of harmonic morphisms

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [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 

  • [BG] Blumenthal, R.M., Getoor, R.K.: Markov processes and potential theory. New York: Academic Press 1968

    Google Scholar 

  • [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 

  • [BH1] Bliedtner, J., Hansen, W.: Markov processes and harmonic spaces. Z. Wahrscheinlichkeitstheorie verw. Geb.42, 309–325 (1978)

    Google Scholar 

  • [BH2] Bliedtner, J., Hansen, W.: Potential Theory. Universitext, Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  • [B] Boboc, N.: Asupra prelungiri aplicatiilor armonice. Ann. Univ. Craiova, Ser. Mat. Fiz. Chim.6, 31–36 (1978)

    Google Scholar 

  • [CC1] Constantinescu, C., Cornea, A.: Compactifications of harmonic spaces. Nagoya Math. J.25, 1–57 (1965)

    Google Scholar 

  • [CC2] Constantinescu, C., Cornea, A.: Potential Theory on Harmonic Spaces. Berlin Heidelberg New York: Springer 1972

    Google Scholar 

  • [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 

  • [DM1] Dellacherie, C., Meyer, P.-A.: Probabilités et potentiel I (Chap. I à IV). Paris: Hermann 1975

    Google Scholar 

  • [DM2] Dellacherie, C., Meyer, P.-A.: Probabilités et potentiel VI (Chap. XII à XV) Paris: Hermann 1987

    Google Scholar 

  • [F1] Fuglede, B.: Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier28, 107–144 (1978)

    Google Scholar 

  • [F2] Fuglede, B.: Invariant characterizations of the fine topology in potential theory. Math. Ann.241, 187–192 (1979)

    Google Scholar 

  • [F3] Fuglede, B.: Harnack sets and openness of harmonic morphisms. Math. Ann.241, 181–186 (1979)

    Google Scholar 

  • [G] Getoor, R.K.: Markov processes: Ray processes and right processes. (Lect. Notes. Math., vol. 444) Berlin Heidelberg New York: Springer 1975

    Google Scholar 

  • [GS] Getoor, R.K., Sharpe, M.J.: Conformal martingales, Invent. Math.16, 271–308 (1972)

    Google Scholar 

  • [K] Kunita, H.: Absolute continuity of Markov processes and generators. Nagoya Math. J.36, 1–26 (1969)

    Google Scholar 

  • [L] Laine, I.: Covering properties of harmonicB1-mapping. Ann. Acad. Sci. Fenn., Ser. Al.1, 309–325 (1975)

    Google Scholar 

  • [McK] McKean, H.P. Jr.: Stochastic integrals. New York: Academic Press 1969

    Google Scholar 

  • [Ø1] Øksendal, B.: Finely harmonic morphisms, Brownian path preserving functions and conformal martingales. Invent. Math.75, 179–187 (1984)

    Google Scholar 

  • [Ø2] Øksendal, B.: Stochastic processes, infinitesimal generators and function theory. In Operators and function theory. S.C. Power (ed.) Dordrecht: Reidel 1985

    Google Scholar 

  • [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 

  • [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 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported in part by NSF Grant DMS 87-21347

Research supported in part by NAVF (Norway) ref. D.93.10.000

Rights and permissions

Reprints and permissions

About this article

Cite this article

Csink, L., Fitzsimmons, P.J. & Øksendal, B. A stochastic characterization of harmonic morphisms. Math. Ann. 287, 1–18 (1990). https://doi.org/10.1007/BF01446874

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01446874

Keywords

Navigation