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Immigration structures associated with Dawson-Watanabe superprocesses

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  • Li, Zeng-Hu

Abstract

The immigration structure associated with a measure-valued branching process may be described by a skew convolution semigroup. For the special type of measure-valued branching process, the Dawson-Watanabe superprocess, we show that a skew convolution semigroup corresponds uniquely to an infinitely divisible probability measure on the space of entrance laws for the underlying process. An immigration process associated with a Borel right superprocess does not always have a right continuous realization, but it can always be obtained by transformation from a Borel right one in an enlarged state space.

Suggested Citation

  • Li, Zeng-Hu, 1996. "Immigration structures associated with Dawson-Watanabe superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 73-86, March.
    • Handle: RePEc:eee:spapps:v:62:y:1996:i:1:p:73-86
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    References listed on IDEAS

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    1. Li, Zeng-Hu, 1992. "Measure-valued branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 249-264, December.
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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. 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.
    3. Hong, Wenming, 2002. "Longtime behavior for the occupation time process of a super-Brownian motion with random immigration," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 43-62, November.
    4. Wenming Hong, 2003. "Large Deviations for the Super-Brownian Motion with Super-Brownian Immigration," Journal of Theoretical Probability, Springer, vol. 16(4), pages 899-922, October.
    5. Hong, Wenming & Li, Zenghu, 2001. "Fluctuations of a super-Brownian motion with randomly controlled immigration," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 285-291, February.

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