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A degenerate stochastic partial differential equation for superprocesses with singular interaction
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  • Published: 26 November 2003

A degenerate stochastic partial differential equation for superprocesses with singular interaction

  • Zenghu Li1,
  • Hao Wang2 &
  • Jie Xiong3,4 

Probability Theory and Related Fields volume 130, pages 1–17 (2004)Cite this article

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  • 9 Citations

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Abstract.

The scaling limit for a class of interacting superprocesses and the associated singular, degenerate stochastic partial differential equation (SDSPDE) are investigated. It is proved that the scaling limit is a coalescing, purely-atomic-measure-valued process which is the unique strong solution of a reconstructed, associated SDSPDE.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Normal University, Beijing, 100875, P.R. China

    Zenghu Li

  2. Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, U.S.A

    Hao Wang

  3. Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, U.S.A

    Jie Xiong

  4. Department of Math. and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

    Jie Xiong

Authors
  1. Zenghu Li
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  2. Hao Wang
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  3. Jie Xiong
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Corresponding author

Correspondence to Hao Wang.

Additional information

The research of this author is supported by NNSF (No. 10131040 and No. 10121101).

The research of this author is supported partially by the research grant of UO.

The research of this author is supported partially by NSA, NSERC, PIms, Lockheed Martin Naval Electronics and Surveillance Systems, Lockheed Martin Canada and VisionSmart through a MITACS center of excellence entitled ‘‘Prediction in Interacting Systems’’.

Mathematics Subject Classification (2000): Primary 60G57, 60H15; Secondary 60J80

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Li, Z., Wang, H. & Xiong, J. A degenerate stochastic partial differential equation for superprocesses with singular interaction. Probab. Theory Relat. Fields 130, 1–17 (2004). https://doi.org/10.1007/s00440-003-0313-z

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  • Received: 05 May 2003

  • Revised: 26 September 2003

  • Published: 26 November 2003

  • Issue Date: September 2004

  • DOI: https://doi.org/10.1007/s00440-003-0313-z

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Keywords

  • coalescing Brownian motion
  • scaling limit
  • purely atomic superprocess
  • interaction
  • stochastic partial differential equation
  • strong solution
  • pathwise uniqueness
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