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Large Deviations for the Super-Brownian Motion with Super-Brownian Immigration

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  • Wenming Hong

    (Beijing Normal University)

Abstract

Local large deviation principles are established in dimensions d≥3 for the super Brownian motion with random immigration X ϱ t , where the immigration rate is governed by the trajectory of another super-Brownian motion ϱ. The speed function is t for d≥4 and t 1/2 for d=3, compared with the existing results, the interesting phenomenon happened in d=4 with speed t (although only the upper large deviation bound is derived here) is just because the structure of this new model: the random immigration “smooth” the critical dimension in some sense. The rate function are characterized by an evolution equation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:4:d:10.1023_b:jotp.0000011999.03918.f7
    DOI: 10.1023/B:JOTP.0000011999.03918.f7
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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.
    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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    Cited by:

    1. Wenming Hong & Ofer Zeitouni, 2007. "A Quenched CLT for Super-Brownian Motion with Random Immigration," Journal of Theoretical Probability, Springer, vol. 20(4), pages 807-820, December.

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