Abstract. In this paper we consider the Laplace transforms of some random series, in particular, the random series derived as the squared L2 norm of a Gaussian stochastic process. Except for some special cases, closed form expressions for Laplace transforms are, in general, rarely obtained. It is the purpose of this paper to show that for many Gaussian random processes the Laplace transform can...

In order to numerically invert Laplace transforms to calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waiting-time cdf) can be computed when the Laplace transform values of component pdf’s (e.g.,...