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Fluctuation limit theorems of immigration superprocesses with small branching

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  • Li, Zenghu
  • Zhang, Mei

Abstract

We establish fluctuation limit theorems of immigration superprocesses with small branching rates. The weak convergence of the processes on a Sobolev space is established, which improves the result of Gorostiza and Li (High density fluctuations of immigration branching particle systems. In: Gorostiza, L.G., Ivanoff, B.G. (Eds.), Stochastic Models, (Ottawa, Ontario, 1998), CMS Conference Proceedings 2000, Series vol. 26, American Mathematical Society, Providence, RI, pp. 159-171). The limiting processes are infinite-dimensional Ornstein-Uhlenbeck type processes.

Suggested Citation

  • Li, Zenghu & Zhang, Mei, 2006. "Fluctuation limit theorems of immigration superprocesses with small branching," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 401-411, February.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:4:p:401-411
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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. Li, Zeng-Hu, 1996. "Immigration structures associated with Dawson-Watanabe superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 73-86, March.
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