2006 Volume 64 Issue 3 Pages 563-579
A class of immigration superprocesses with dependent spatial motion for deterministic immigration rate is considered, and we discuss a convergence problem for the rescaled processes. When the immigration rate converges to a non-vanishing deterministic one, then we can prove that under a suitable scaling, the rescaled immigration superprocesses associated with SDSM converge to a class of immigration superprocesses associated with coalescing spatial motion in the sense of probability distribution on the space of measure-valued continuous paths. This scaled limit not only provides with a new class of superprocesses but also gives a new type of limit theorem.
