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Particle representations of superprocesses with dependent motions

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  • Temple, Kathryn E.

Abstract

We establish Donnelly-Kurtz-type particle representations for a class of superprocesses with dependent spatial motions, and for a sequence of such superprocesses we prove convergence of the finite-dimensional distributions given convergence of the motion processes. As special cases, we construct a superprocess with coalescing spatial motion (SCSM) and a superprocess with dependent spatial motion (SDSM), where the underlying motion processes are one-dimensional coalescing and dependent Brownian motions, respectively. Under suitable conditions on the functions governing the interactions, we show convergence in distribution in of a sequence of SDSMs to an SCSM.

Suggested Citation

  • Temple, Kathryn E., 2010. "Particle representations of superprocesses with dependent motions," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2174-2189, November.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:11:p:2174-2189
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    References listed on IDEAS

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    1. 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.
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