A Diffusion Equation for the Density of the Ratio of Two Jointly Distributed Gaussian Variables and the Exponential Analysis Problem

Authors:
Piero Barone
Affiliations:
p.barone@iac.cnr.it and piero.barone@gmail.com
Venue:
SIAM Journal on Scientific Computing
Year:
2012

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Abstract

It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a nonstationary diffusion equation. Implications of this result for adaptive kernel density estimation of the condensed density of the generalized eigenvalues of a random matrix pencil useful for solving the exponential analysis problem are discussed.