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A characterization ofh-Brownian motion by its exit distributions
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  • Published: March 1992

A characterization ofh-Brownian motion by its exit distributions

  • Zoran Vondraček1 

Probability Theory and Related Fields volume 92, pages 41–50 (1992)Cite this article

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Summary

LetX h be anh-Brownian motion in the unit ballD⊃R d withh harmonic, such that the representing measure ofh is not singular with respect to the surface measure on ∂D. IfY is a continuous strong Markov process inD with the same killing distributions asX h, thenY is a time change ofX h. Similar results hold in simply connected domains inC provided with either the Martin or the Euclidean boundary.

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References

  1. Blumenthal, R.M., Getoor, R.K.: Markov processes and potential theory. New York: Academic Press 1968

    Google Scholar 

  2. Doob, J.L.: Classical potential theory and its probabilistic counterpart. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  3. Fitzsimmons, P.J.: Markov processes with identical hitting probabilities. Math. Z.192, 547–554 (1986)

    Google Scholar 

  4. Fitzsimmons, P.J., Getoor, R.M., Sharpe, M.J.: The Blumenthal-Getoor-McKean theorem revisited. In: Cinlar, E., Chung, K.L., Getoor, R.K. (eds.) Seminar on stochastic processes 1989. Boston: Birkhäuser 1990

    Google Scholar 

  5. Glover, J.: Markov processes with identical hitting probabilities. TAMS275 (1), 131–141 (1983)

    Google Scholar 

  6. Glover, J.: Markov processes with identical last exit distributions. Z. Wahrscheinlichkeitstheor. Verw. Geb.59, 67–75 (1982)

    Google Scholar 

  7. Ohtsuka, M.: Dirichlet problem, extremal length and prime ends. New York: Van Nostrand 1970

    Google Scholar 

  8. Øksendal, B., Stroock, D.W.: A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations, translations and dilatations. Ann. Inst. Fourier32, (4) 221–232 (1982)

    Google Scholar 

  9. Rao, M.: Brownian motion and classical potential theory. Lecture Notes Series, No. 47. Matematisk Institut, Aarhus University, Aarhus. 1977

    Google Scholar 

  10. Sharpe, M.J.: General theory of Markov processes. New York: Academic Press 1988

    Google Scholar 

  11. Vondraček, Z.: A characterization of Brownian motion in a Lipschitz domain by its killing distributions. J. Theor. Probab.4, (2) 457–464 (1991)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Zagreb, P.O. Box 635, Yu-41000, Zagreb, Croatia

    Zoran Vondraček

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  1. Zoran Vondraček
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Vondraček, Z. A characterization ofh-Brownian motion by its exit distributions. Probab. Th. Rel. Fields 92, 41–50 (1992). https://doi.org/10.1007/BF01205235

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  • Received: 23 November 1990

  • Revised: 19 September 1991

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01205235

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Keywords

  • Stochastic Process
  • Probability Theory
  • Markov Process
  • Mathematical Biology
  • Surface Measure
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