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

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

2011-02-11

arxiv.org/abs/1102.2354v2

Mathematics

Statistics Theory

25 pages, 2 figures, Theorem 3.3 has been added

Scientific paper

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.

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