  We present a general class of spatio-temporal stochastic processes describing
the causal evolution of a positive-valued field in space and time. The field
construction is based on independently scattered random measures of Levy type
whose weighted amplitudes are integrated within a causality cone. General
n-point correlations are derived in closed form. As a special case of the
general framework, we consider a causal multiscaling process in space and time
in more detail. The latter is derived from, and completely specified by,
power-law two-point correlations, and gives rise to scaling behaviour of both
purely temporal and spatial higher-order correlations. We further establish the
connection to classical multifractality and prove the multifractal nature of
the coarse-grained field amplitude.
