  Sojourn measures have played a crucial role in the description of geometric
characteristics of random surfaces, providing information on level crossing and
possible extreme values. An extensive literature can be found in the field of
stochastic processes, and statistics. Particularly, the asymptotic behavior,
when the window size grows, of the volume of excursion sets has been widely
investigated. The present work addresses this problem in the spatiotemporal
process context, considering the case of long range dependence (LRD) Gaussian
and chi--square random fields. Specifically, a reduction theorem is derived.
Some central and non-central limit results can then be established for LRD
spatiotemporal random fields constructed by subordination from Gaussian and
chi-square random fields.
