We study the scaling limit of random fields which are solutions of a n
on-linear partial differential equation, known as the Burgers equation
, under stochastic initial conditions. These are assumed to be of a no
n-local shot noise type and driven by a Cox process. Previous work by
Bulinskii and Molchanov (1991), Surgailis and Woyczynski (1993a), and
Funaki et al. (1994) concentrated on the case of local shot noise data
which permitted use of techniques from the theory of random fields wi
th finite range dependence. Those are not available for the non-local
case being considered in this paper. Burgers' equation is known to des
cribe various physical phenomena such as non-linear and shock waves, d
istribution of self-gravitating matter in the universe, and other flow
satisfying conservation laws (see e.g. Woyczynski (1993)).