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Central limit theorems for supercritical superprocesses

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  • Ren, Yan-Xia
  • Song, Renming
  • Zhang, Rui

Abstract

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and unifies all the central limit theorems obtained recently in Miłoś (2012) and Ren et al. (2014) for supercritical super Ornstein–Uhlenbeck processes. The advantage of this central limit theorem is that it allows us to characterize the limit Gaussian field. In the case of supercritical super Ornstein–Uhlenbeck processes with non-spatially dependent branching mechanisms, our central limit theorem reveals more independent structures of the limit Gaussian field.

Suggested Citation

  • Ren, Yan-Xia & Song, Renming & Zhang, Rui, 2015. "Central limit theorems for supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 428-457.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:2:p:428-457
    DOI: 10.1016/j.spa.2014.09.014
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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. Cohn, H. & Hering, H., 1983. "Inhomogeneous Markov branching processes: Supercritical case," Stochastic Processes and their Applications, Elsevier, vol. 14(1), pages 79-91, January.
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    Cited by:

    1. Li Wang, 2018. "Central Limit Theorems for Supercritical Superprocesses with Immigration," Journal of Theoretical Probability, Springer, vol. 31(2), pages 984-1012, June.
    2. Liu, Rongli & Ren, Yan-Xia & Song, Renming, 2022. "Convergence rate for a class of supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 286-327.
    3. Liu, Rongli & Ren, Yan-Xia & Song, Renming & Sun, Zhenyao, 2023. "Subcritical superprocesses conditioned on non-extinction," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 498-534.

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