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Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions
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  • Published: 18 June 2003

Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions

  • Donald A. Dawson1 &
  • Zenghu Li2 

Probability Theory and Related Fields volume 127, pages 37–61 (2003)Cite this article

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  • 22 Citations

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Abstract.

A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional excursions.

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References

  1. Dawson, D.A.: Measure-Valued Markov Processes. Lect. Notes. Math. 1541, Berlin: Springer-Verlag, 1993, pp. 1–260

  2. Dawson, D.A., Vaillancourt, J., Wang, H.: Stochastic partial differential equations for a class of measure-valued branching diffusions in a random medium. Ann. Inst. Henri Poincare, Probabilités and Statistiques 36, 167–180 (2000)

    Google Scholar 

  3. Dawson, D.A., Li, Z.H., Wang, H.: Superprocesses with dependent spatial motion and general branching densities. Elect. J. Probab. (25) 6, 1–33 (2001)

    Google Scholar 

  4. Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence. New York: Wiley, 1986

  5. Fu, Z.F., Li, Z.H.: Measure-valued diffusions and stochastic equations with Poisson process. Osaka J. Math., 2003, submitted, ps and pdf files: math.bnu.edu.cn/˜lizh

  6. Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North-Holland/Kodansha, Amsterdam/Tokyo, 1989

  7. Konno, N., Shiga, T.: Stochastic partial differential equations for some measure-valued diffusions. Probab. Theory Related Fields 79, 201–225 (1988)

    MathSciNet  MATH  Google Scholar 

  8. Li, Z.H.: Skew convolution semigroups and related immigration processes. Theory Probab. Appl. 46, 274–296 (2002)

    Article  MATH  Google Scholar 

  9. Li, Z.H., Shiga, T.: Measure-valued branching diffusions: immigrations, excursions and limit theorems. J. Math. Kyoto Univ. 35, 233–274 (1995)

    MathSciNet  MATH  Google Scholar 

  10. Pitman, J., Yor, M.: A decomposition of Bessel bridges. Z. Wahrsch. verw. Geb. 59, 425–457 (1982)

    MATH  Google Scholar 

  11. Reimers, M.: One dimensional stochastic differential equations and the branching measure diffusion. Probab. Theory Related Fields 81, 319–340 (1989)

    MathSciNet  MATH  Google Scholar 

  12. Shiga, T.: A stochastic equation based on a Poisson system for a class of measure-valued diffusion processes. J. Math. Kyoto Univ. 30, 245–279 (1990)

    MathSciNet  MATH  Google Scholar 

  13. Shiga, T., Watanabe, S.: Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrsch. verw. Geb. 27, 37–46 (1973)

    MATH  Google Scholar 

  14. Walsh, J.B.: An Introduction to Stochastic Partial Differential Equations. In: Lect. Notes Math. 1180, Springer-Verlag, 1986, pp. 265–439

  15. Wang, H.: State classification for a class of measure-valued branching diffusions in a Brownian medium. Probab. Theory Related Fields 109, 39–55 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, H.: A class of measure-valued branching diffusions in a random medium. Stochastic Anal. Appl. 16, 753–786 (1998)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Canada, K1S 5B6

    Donald A. Dawson

  2. Department of Mathematics, Beijing Normal University, Beijing, 100875, People's Republic of China

    Zenghu Li

Authors
  1. Donald A. Dawson
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  2. Zenghu Li
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Corresponding author

Correspondence to Zenghu Li.

Additional information

Supported by an NSERC Research Grant and a Max Planck Award.

Supported by the NSFC (No. 10121101 and No. 10131040).

Mathematics Subject Classification (2000): Primary 60J80; Secondary 60G57 60H20

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Cite this article

Dawson, D., Li, Z. Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions. Probab. Theory Relat. Fields 127, 37–61 (2003). https://doi.org/10.1007/s00440-003-0278-y

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  • Received: 06 August 2002

  • Revised: 27 March 2003

  • Published: 18 June 2003

  • Issue Date: September 2003

  • DOI: https://doi.org/10.1007/s00440-003-0278-y

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Keywords

  • Superprocess
  • Dependent spatial motion
  • Immigration
  • Excursion
  • Stochastic equation
  • Poisson random measure
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