  Traditional interpolation techniques for particle tracking include binning
and convolutional formulas that use pre-determined (i.e., closed-form,
parameteric) kernels. In many instances, the particles are introduced as point
sources in time and space, so the cloud of particles (either in space or time)
is a discrete representation of the Green's function of an underlying PDE. As
such, each particle is a sample from the Green's function; therefore, each
particle should be distributed according to the Green's function. In short, the
kernel of a convolutional interpolation of the particle sample "cloud" should
be a replica of the cloud itself. This idea gives rise to an iterative method
by which the form of the kernel may be discerned in the process of
interpolating the Green's function. When the Green's function is a density,
this method is broadly applicable to interpolating a kernel density estimate
based on random data drawn from a single distribution. We formulate and
construct the algorithm and demonstrate its ability to perform kernel density
estimation of skewed and/or heavy-tailed data including breakthrough curves.
