A Markov process for an infinite interacting particle system in the continuum

Kozitsky Y, Röckner M. A Markov process for an infinite interacting particle system in the continuum. Electronic Journal of Probability . 2021;26:1-53.An infinite system of point particles placed in R-d is studied. Its constituents perform random jumps (walks) with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states of the system are locally finite subsets of R-d, which can also be interpreted as locally finite Radon measures. The set of all such measures Gamma is equipped with the vague topology and the corresponding Borel sigma-field. For a special class P-exp of (sub-Poissonian) probability measures on Gamma, we prove the existence of a unique family {P-t,P-mu : t >= 0, mu is an element of P-exp} of probability measures on the space of cadlag paths with values in that solves a restricted initial-value martingale problem for the mentioned system. Thereby, a Markov process with cadlag paths is specified which describes the stochastic dynamics of this particle system