Occupation time processes of super-Brownian motion with cut-off branching
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In this article we investigate a class of superprocess with cut-off branching, studying the long-time behavior of the occupation time process. Persistence of the process holds in all dimensions. Central-limit-type theorems are obtained, and the scales are dimension dependent. The Gaussian limit holds only when d ≤ 4. In dimension one, a full large deviation principle is established and the rate function is identified explicitly. Our result shows that the super-Brownian motion with cut-off branching in dimension one has many features that are similar to super-Brownian motion in dimension three.
2004 ◽
Vol 41
(4)
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pp. 984-997
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2008 ◽
Vol 11
(01)
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pp. 53-71
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2004 ◽
Vol 41
(01)
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pp. 187-201
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2004 ◽
Vol 41
(1)
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pp. 187-201
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Longtime behavior for the occupation time process of a super-Brownian motion with random immigration
2002 ◽
Vol 102
(1)
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pp. 43-62
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2010 ◽
Vol 10
(03)
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pp. 315-339
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