Immigration

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Abstract

A class of immigration superprocesses (IMS) with dependent spatial motion is considered. When the immigration rate converges to a non‐vanishing deterministic one, we can prove that under a suitable scaling, the rescaled immigration superprocesses converge to a class of IMS with coalescing spatial motion in the sense of probability distribution on the space of measure‐ valued continuous paths. This scaled limit does not only provide with a new type of limit theorem but also gives a new class of superprocesses. Other related limits for superprocesses with dependent spatial motion are summarized.