Distributions of particle displacements via higher-order moment functions

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Abstract
Concern is with phenomena that are moving and developing in time. Indistinguishable particles are displaced independently, with successive displacements possibly correlated. One wishes to estimate 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 in the case that the original placements of the particles are homogeneous Poisson. Surprisingly then the cumulant density is essentially the probability density.