A diffusion equation for the density of the ratio of two jointly distributed Gaussian variables and the numerical inversion of Laplace transform
Provides a theoretical result for a specific statistical distribution, but the practical impact is limited and incremental.
The paper derives a diffusion equation for the density of the ratio of two jointly Gaussian variables with equal variance, and discusses its application to kernel density estimation for numerical inversion of Laplace transforms. No concrete numerical results are provided.
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.