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Longtime behavior for the occupation time process of a super-Brownian motion with random immigration

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  • Hong, Wenming

Abstract

Longtime behavior for the occupation time of a super-Brownian motion with immigration governed by the trajectory of another super-Brownian motion is considered. Central limit theorems are obtained for dimensions d[greater-or-equal, slanted]3 that lead to some Gaussian random fields: for 3[less-than-or-equals, slant]d[less-than-or-equals, slant]5, the field is spatially uniform, which is caused by the randomness of the immigration branching; for d[greater-or-equal, slanted]7, the covariance of the limit field is given by the potential operator of the Brownian motion, which is caused by the randomness of the underlying branching; and for d=6, the limit field involves a mixture of the two kinds of fluctuations. Some extensions are made in higher dimensions. An ergodic theorem is proved as well for dimension d=2, which is characterized by an evolution equation.

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  • 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.
    • Handle: RePEc:eee:spapps:v:102:y:2002:i:1:p:43-62
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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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