Distributions of particle displacements via higher-order moment functions

Discusses phenomena that are moving and developing in time. Indistinguishable particles are displaced independently, with successive displacements possibly correlated. The author estimates the joint probability distribution of those displacements. It is shown how this may be done via estimates of higher-order cumulant densities and spectra. The results simplify for the case that the original placements of the particles are homogeneous Poisson. It is found that the cumulant density is essentially the probability density