Superprocesses with interaction and immigration

We construct a class of superprocesses with interactive branching, immigration mechanisms, and spatial motion. It arises as the limit of a sequence of interacting branching particle systems with immigration, which generalizes a result of Méléard and Roelly (1993) established for a superprocess with interactive spatial motion. The uniqueness in law of the superprocess is established under certain conditions using the pathwise uniqueness of an SPDE satisfied by its corresponding distribution function process. This generalizes the recent work of Mytnik and Xiong (2015), where the result for a super-Brownian motion with interactive immigration mechanisms was obtained. An extended Yamada-Watanabe argument is used in the proving of pathwise uniqueness.