Laplace Transforms of Improper Random Variables
Janhavi Prabhu, Myron Hlynka
TL;DR
This paper explores the use of Laplace transforms to analyze improper random variables, focusing on their probabilistic interpretation and applications to queueing theory, especially busy periods.
Contribution
It provides a novel probabilistic interpretation of Laplace transforms for improper random variables and applies this to analyze busy periods in queueing models.
Findings
Interpretation of $L(0)$ in specific cases
Application to busy periods in queueing models
Enhanced understanding of improper random variables
Abstract
The probabilistic interpretation of Laplace transforms is used to help to describe the Laplace Transform of improper random variables. In particular, busy periods in queueing models are examined. The value of is explained in certain special cases.
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