Advances and Applications in Statistics
Volume 6, Issue 2, Pages 145 - 205
(August 2006)
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A CERTAIN CLASS OF IMMIGRATION SUPERPROCESSES AND ITS LIMIT THEOREM
Isamu Doku (Japan)
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Abstract: We consider a class of Dawson-Li superprocesses with deterministic immigration, and discuss a convergence problem for the rescaled processes. When such a superprocess associated with dependent spatial motion is given, its rescaled process becomes again an immigration superprocess of the same kind. Then we prove that under a suitable scaling, the rescaled immigration superprocesses converge to a superprocess with coalescing spatial motion in the sense of probability distribution on the space of measure-valued continuous paths. |
Keywords and phrases: deterministic immigration superprocess, rescaled limit, superprocesses with dependent spatial motion and coalescing spatial motion. |
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