  We introduce a new approximate multiresolution analysis (MRA) using a single
Gaussian as the scaling function, which we call Gaussian MRA (GMRA). As an
initial application, we employ this new tool to accurately and efficiently
compute the probability density function (PDF) of the product of independent
random variables. In contrast with Monte-Carlo (MC) type methods (the only
other universal approach known to address this problem), our method not only
achieves accuracies beyond the reach of MC but also produces a PDF expressed as
a Gaussian mixture, thus allowing for further efficient computations. We also
show that an exact MRA corresponding to our GMRA can be constructed for a
matching user-selected accuracy.
