A diffusion equation for the density of the ratio of two jointly distributed Gaussian variables and the numerical inversion of Laplace transform

Abstract

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.

25 pages, 2 figures, Theorem 3.3 has been added

References in corpus (3)

• Kernel density estimation via diffusion
• A new transform for solving the noisy complex exponentials approximation problem
• Computational aspects and applications of a new transform for solving the complex exponentials approximation problem

Cited by in corpus (2)

• On the condensed density of the generalized eigenvalues of pencils of Hankel Gaussian random matrices and applications
• A black box method for solving the complex exponentials approximation problem