  This paper is focused on a class of spatial birth and death process of the
Euclidean space where the birth rate is constant and the death rate of a given
point is the shot noise created at its location by the other points of the
current configuration for some response function $f$. An equivalent view point
is that each pair of points of the configuration establishes a random
connection at an exponential time determined by $f$, which results in the death
of one of the two points. We concentrate on space-motion invariant processes of
this type. Under some natural conditions on $f$, we construct the unique
time-stationary regime of this class of point processes by a coupling argument.
We then use the birth and death structure to establish a hierarchy of balance
integral relations between the factorial moment measures. Finally, we show that
the time-stationary point process exhibits a certain kind of repulsion between
its points that we call $f$-repulsion.
