We consider a space-time random field on Rd × R given as an integral of
a kernel function with respect to a Lévy basis with a convolution equivalent
Lévy measure. The field obeys causality in time and is thereby not continuous along
the time-axis. For a large class of such random fields we study the tail
behaviour of certain functionals of the field. It turns out that the tail is
asymptotically equivalent to the right tail of the underlying Lévy measure.
Particular examples are the asymptotic probability that there is a time-point
and a rotation of a spatial object with fixed radius, in which the field
exceeds the level x, and that there
is a time-interval and a rotation of a spatial object with fixed radius, in
which the average of the field exceeds the level x.