On spline regularized inversion of noisy Laplace transforms

Numerical Inversion of Laplace Transforms of Probability Distributions

The purpose of this document is to summarize main points of the paper, “Numerical Inversion of Laplace Transforms of Probability Distributions”, and provide R code for the Euler method that is described in the paper. The code is used to invert the Laplace transform of some popular functions. Context Laplace transform is a useful mathematical tool that one must be familiar with, while doing appl...

Numerical Inversion of Multidimensional Laplace Transforms by the Laguerre Method

Numerical transform inversion can be useful to solve stochastic models arising in the performance evaluation of telecommunications and computer systems. We contribute to this technique in this paper by extending our recently developed variant of the Laguerre method for numerically inverting Laplace transforms to multidimensional Laplace transforms. An important application of multidimensional i...

Computing Laplace Transforms for Numerical Inversion Via Continued Fractions

It is often possible to effectively calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s ) by numerically inverting Laplace transforms. However, to do so it is necessary to compute the Laplace transform values. Unfortunately, convenient explicit expressions for required transforms are often unavailable for component pdf’s in a probability model. In that e...

A note on the comparison between Laplace and Sumudu transforms

Notes on Numerical Laplace Inversion

The main idea behind the Laplace transformation is that we can solve an equation (or system of equations) containing differential and integral terms by transforming the equation in time (t) domain into Laplace (2) domain. For example, we can use Laplace transforms to turn an initial value problem into an algebraic problem which is easier to solve. After we solved the problem in Laplace domain w...