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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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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DOI: https://doi.org/10.1007/s00440-003-0313-z
Keywords
- coalescing Brownian motion
- scaling limit
- purely atomic superprocess
- interaction
- stochastic partial differential equation
- strong solution
- pathwise uniqueness