  We extend the celebrated Rothschild and Stiglitz (1970) definition of
Mean-Preserving Spreads to a dynamic framework. We adapt the original integral
conditions to transition probability densities, and give sufficient conditions
for their satisfaction. We then prove that a specific nonlinear scalar
diffusion process, super-diffusive ballistic noise, is the unique process that
satisfies the integral conditions among a broad class of processes. This
process can be generated by a random superposition of linear Markov processes
with constant drifts. This exceptionally simple representation enables us to
systematically revisit, by means of the properties of Dynamic Mean-Preserving
Spreads, four workhorse economic models originally based on White Gaussian
Noise.
