Existence and spatial limit theorems for lattice and continuum particle systems

We give a general existence result for interacting particle systems with local interactions and bounded jump rates but noncompact state space at each site. We allow for jump events at a site that affect the state of its neighbours. We give a law of large numbers and functional central limit theorem for additive set functions taken over an increasing family of subcubes of $Z^d$. We discuss application to marked spatial point processes with births, deaths and jumps of particles, in particular examples such as continuum and lattice ballistic deposition and a sequential model for random loose sphere packing.