Interactive infinite Markov particle systems with jumps

Abstract

In [2] we investigated independent infinite Markov particle systems as measure-valued Markov processes with jumps, and we gave sample path properties and martingale characterizations. In particular, we investigated the exponent of Hölder-right continuity in case that the motion process is absorbing α-stable motion on (0,∞) with 0 < α < 2, that is, time-changed absorbing Brownian motions on (0,∞) by the increasing α/2-stable Lévy processes.In the present paper we shall extend the results to the case of simple interactive infinite Markov particle systems. We also consider the absorbing stable motion on a half space H = Rd−1 × (0,∞) as a motion process.