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

Wenming Hong

Stochastic Processes and their Applications, 2002, vol. 102, issue 1, 43-62

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.

Keywords: Super-Brownian; motion; Random; immigration; Central; limit; theorem; Ergodic; theorem; Evolution; equation (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (2)

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