  An infinite system of point particles placed in $\mathds{R}^d$ is studied.
Its constituents perform random jumps 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 $\mathds{R}^d$, 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 $\mathcal{P}_{\rm exp}$ of
(sub-Poissonian) probability measures on $\Gamma$, we prove the existence of a
unique family $\{P_{t,\mu}: t\geq 0, \ \mu \in \mathcal{P}_{\rm exp}\}$ of
probability measures on the space of cadlag paths with values in $\Gamma$ 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.
