Independent Infinite Markov Particle Systems with Jumps

Seiji Hiraba
Theory of Stochastic Processes
Vol.18 (34), no.1, 2012, pp.65-85
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 H\"older 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 L\'evy processes.