6 papers · 1 filter
Colored Markov-Modulated Brownian Motion for Preemptive Workload Stacks
Maria Laura Battagliola, Eduardo Medina-Valdés, Oscar Peralta
We develop a colored Markov-modulated Brownian motion model for diffusion-scale systems in which newly created work preempts the active layer, occupies the top of an ordered stack,…
Equivalence and Separation for Multivariate Matrix-Exponential and Phase-Type Distribution Classes
Oscar Peralta
We resolve two questions left open by Bladt and Nielsen (2010) concerning multivariate families of matrix-exponential and phase-type distributions. First, in the matrix-exponential…
Optimization-Free Concentrated Matrix-Exponentials
Maria Laura Battagliola, Oscar Peralta
Near-deterministic positive delays require highly concentrated distributions, but phase-type models are constrained by the Erlang variance limit. While matrix-exponential distribut…
Matrix Representations for Scale Functions of Spectrally Negative Lévy Processes with Rational Jumps
Osvaldo Angtuncio Hernández, Oscar Peralta
For a spectrally negative Lévy process with Laplace transform , the -scale function is characterized as the function whose Laplace transform is . It has…
Rational arrival processes with strictly positive densities need not be Markovian
Oscar Peralta
Telek (2022) asked whether a rational arrival process (RAP), specified by matrices and and an initial row vector , with strictly positive joint densities and a…
Approximations of semi-Markov processes and insurance policy valuation
Martin Bladt, Andreea Minca, Oscar Peralta
Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state-space. We develop approximat…