  An infinite system of point particles performing random jumps in
$\mathds{R}^d$ with repulsion is studied. The states of the system are
probability measures on the space of particle's configurations. The result of
the paper is the construction of the global in time evolution of states with
the help of the corresponding correlation functions. It is proved that for each
initial sub-Poissonian state $\mu_0$, the constructed evolution $\mu_0 \mapsto
\mu_t$ preserves this property. That is, $\mu_t$ is sub-Poissonian for all
$t>0$.
