Related papers: Laplace Transform Effectiveness in the MGinf Queue…
We analyze the so-called Shortest Queue First (SQF) queueing discipline whereby a unique server addresses queues in parallel by serving at any time that queue with the smallest workload. Considering a stationary system composed of two…
The Laplace transform is a useful and powerful analytic tool with applications to several areas of applied mathematics, including differential equations, probability and statistics. Similarly to the inversion of the Fourier transform,…
This paper concentrates on the general birth-death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth-death processes with two-type catastrophes are is successfully…
In this paper, we analyze a polling system on a circle with. Random batches of customers arrive at a circle, where each customer, independently, obtains a location according to a general distribution. A single server cyclically travels over…
In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its…
The Pareto distribution plays a crucial role in various disciplines, necessitating robust goodness-of-fit tests for its validation. This article introduces a novel tests based on Stein's characterization and the Laplace transform, offering…
An exact formula for the equilibrium M/U/1 waiting time density is now effectively known. What began as a numeric exploration became a symbolic banquet. Inverse Laplace transforms provided breadcrumbs in the trail; delay differential…
The Laplace transform in Komatsu ultradistributions is considered. Also, conditions are given under which an analytic function is a Laplace transformation of an ultradistribution.
This paper studies the workload distribution of a finite-capacity queue driven by a spectrally one-sided Markov additive process (MAP). Our main result provides the Laplace-Stieltjes transform of the workload at an exponentially distributed…
It is a very hard task to compute an exact solution for the differential equations, with differences, system that allows the determination of the M|M|m|m system transient probabilities. The respective complexity grows with m. The…
This paper investigates an insurance model with a finite number of major clients and a large number of small clients, where the dynamics of the latter group are modeled by a spectrally positive L\'evy process. We begin by analyzing this…
In this paper, we present a novel test for determining equality in distribution of matrix distributions. Our approach is based on the integral squared difference of the empirical Laplace transforms with respect to the noncentral Wishart…
Consider a Markov chain with finite state $\{0, 1, ..., d\}$. We give the generation functions (or Laplace transforms) of absorbing (passage) time in the following two situations : (1) the absorbing time of state $d$ when the chain starts…
A popular method to compute first-passage probabilities in continuous-time Markov chains is by numerically inverting their Laplace transforms. Past decades, the scientific computing community has developed excellent numerical methods for…
Energy forecasting is pivotal in energy systems, by providing fundamentals for operation, with different horizons and resolutions. Though energy forecasting has been widely studied for capturing temporal information, very few works…
In this paper, we study queueing systems with delayed information that use a generalization of the multinomial logit choice model as its arrival process. Previous literature assumes that the functional form of the multinomial logit model is…
In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed…
We focus on a particular connection between queueing and risk models in a multi-dimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case…
The Laplace transform is an algebraic method that is widely used for analyzing physical systems by either solving the differential equations modeling their dynamics or by evaluating their transfer function. The dynamics of the given system…
Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is…