A diffusion equation for the density of the ratio of two jointly   distributed Gaussian variables and the numerical inversion of Laplace   transform
  It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a non stationary diffusion equation. Implications of this result for kernel density estimation of the condensed density of the generalized eigenvalues of a random matrix pencil useful for the numerical inversion of the Laplace transform is discussed. 
Piero Barone
math.ST math.NA stat.TH