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Particle representations of superprocesses with dependent motions

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Abstract

We establish Donnelly-Kurtz-type particle representations for a class of superprocesses with dependent spatial motions, and for a sequence of such superprocesses we prove convergence of the finite-dimensional distributions given convergence of the motion processes. As special cases, we construct a superprocess with coalescing spatial motion (SCSM) and a superprocess with dependent spatial motion (SDSM), where the underlying motion processes are one-dimensional coalescing and dependent Brownian motions, respectively. Under suitable conditions on the functions governing the interactions, we show convergence in distribution in of a sequence of SDSMs to an SCSM.

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