Independent infinite Markov particle systems with jumps

We investigate independent infinite Markov particle systems (IIMPSs) as measure-valued Markov processes with jumps. We shall give sample path properties and martingale characterizations. In particular, we investigate the Hölder right continuity exponent in the case where each particle participates in the absorbing $\alpha$-stable motion on $(0,\infty)$ with $0<\alpha<2$, that is, the time-changed absorbing Brownian motion on $(0,\infty)$ by the increasing $\alpha/2$-stable Lévy processes.