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Discontinuous superprocesses with dependent spatial motion

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  • He, Hui

Abstract

We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the particles are not independent. The main work is to solve the martingale problem. When we turn to the uniqueness of the process, we generalize the localization method introduced by [Daniel W. Stroock, Diffusion processes associated with Lévy generators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 32 (1975) 209-244] to the measure-valued context. As for existence, we use particle system approximation and a perturbation method. This work generalizes the model introduced in [Donald A. Dawson, Zenghu Li, Hao Wang, Superprocesses with dependent spatial motion and general branching densities, Electron. J. Probab. 6 (25) (2001) 33 pp (electronic)] where a quadratic branching mechanism was considered. We also investigate some properties of the process.

Suggested Citation

  • He, Hui, 2009. "Discontinuous superprocesses with dependent spatial motion," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 130-166, January.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:1:p:130-166
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    References listed on IDEAS

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    1. El Karoui, Nicole & Roelly, Sylvie, 1991. "Propriétés de martingales, explosion et représentation de Lévy--Khintchine d'une classe de processus de branchement à valeurs mesures," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 239-266, August.
    2. 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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    Cited by:

    1. Xiong, Jie & Yang, Xu, 2016. "Superprocesses with interaction and immigration," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3377-3401.

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