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Superprocesses with Dependent Spatial Motion and General Branching Densities

Author

Listed:
  • Donald A. Dawson

    (School of Mathematics and Statistics, Carleton University)

  • Zenghu Li

    (Department of Mathematics, Beijing Normal University)

  • Hao Wang

    (Department of Mathematics, University of Oregon)

Abstract

We constructs a class of seperprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching density is given by an arbitary bounded non-negative Borel function, and the superprocess is characterized by a martingale problem as a diffusion process with state space "M (R)", improving and extending considerably the construction of Wang (1997, 1998). It is then proved in a spatial case that a suitable rescaled process of the superprocess converges to the usual super Brownian motion. An extention to measure-valued branching catalysts is also discussed.

Suggested Citation

  • Donald A. Dawson & Zenghu Li & Hao Wang, 2001. "Superprocesses with Dependent Spatial Motion and General Branching Densities," RePAd Working Paper Series lrsp-TRS346, Département des sciences administratives, UQO.
    • Handle: RePEc:pqs:wpaper:0032005
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    File URL: http://www.repad.org/ca/on/lrsp/TRS346.pdf
    File Function: First version, 2001
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    Citations

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    Cited by:

    1. D. A. Dawson & Z. Li & X. Zhou, 2004. "Superprocesses with Coalescing Brownian Spatial Motion as Large-Scale Limits," Journal of Theoretical Probability, Springer, vol. 17(3), pages 673-692, July.
    2. Li, Zenghu & Xiong, Jie & Zhang, Mei, 2010. "Ergodic theory for a superprocess over a stochastic flow," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1563-1588, August.
    3. Mei Zhang, 2011. "Central Limit Theorems for a Super-Diffusion over a Stochastic Flow," Journal of Theoretical Probability, Springer, vol. 24(1), pages 294-306, March.
    4. He, Hui, 2009. "Discontinuous superprocesses with dependent spatial motion," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 130-166, January.
    5. Gill, Hardeep S., 2009. "Superprocesses with spatial interactions in a random medium," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 3981-4003, December.
    6. Temple, Kathryn E., 2010. "Particle representations of superprocesses with dependent motions," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2174-2189, November.

    More about this item

    Keywords

    superprocesses; interacting-branching particle system; diffusion process; martingale problem; dual process; rescaled limit; measure-valued catalyst;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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