Particle representations of superprocesses with dependent motions

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 DP(R)[0,∞)DP(R)[0,∞) of a sequence of SDSMs to an SCSM.