Non-autonomous interacting particle systems in continuum
A conservative Feller evolution on continuous bounded functions is constructed from a weakly continuous, time-inhomogeneous transition function describing a pure jump process on a locally compact Polish space. The transition function is assumed to satisfy a Foster-Lyapunov type condition. The results are applied to interacting particle systems in continuum, in particular to general birth-and-death processes (including jumps). Particular examples such as the BDLP and Dieckmann-Law model are considered in the end.
Key words: Interacting particle systems, Feller evolution, pure jump process, configuration space, Foster-Lyapunov criterion, Kolmogorov equation.