  We study a model of an infinite system of point particles in $\mathds{R}^d$
performing random jumps with attraction. The system's states are probability
measures on the space of particle configurations, and their evolution is
described by means of Kolmogorov and Fokker-Planck equations. Instead of
solving these equations directly we deal with correlation functions evolving
according to a hierarchical chain of differential equations, derived from the
Kolmogorov equation. Under quite natural conditions imposed on the jump kernels
-- and analyzed in the paper -- we prove that this chain has a unique classical
sub-Poissonian solution on a bounded time interval. This gives a partial answer
to the question whether the sub-Poissonicity is consistent with any kind of
attraction. We also discuss possibilities to get a complete answer to this
question.
