Oscar Peralta

collaborators

8 papers

math.PR2026

Colored Markov-Modulated Brownian Motion for Preemptive Workload Stacks

Maria Laura Battagliola, Eduardo Medina-ValdÃ©s, 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,…

math.PR2026

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…

math.PR2026

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…

math.PR2026

Matrix Representations for Scale Functions of Spectrally Negative LÃ©vy Processes with Rational Jumps

Osvaldo Angtuncio HernÃ¡ndez, Oscar Peralta

For a spectrally negative LÃ©vy process with Laplace transform $I ¨ $ , the $q$ -scale function is characterized as the function whose Laplace transform is $(I ¨ (\cdot) - q)^{- 1}$ . It has…

math.PR2026

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 $G_{0}$ and $G_{1}$ and an initial row vector $I^½$ , with strictly positive joint densities and a…

math.ST2025

Assessing continuous common-shock risk through matrix distributions

Martin Bladt, Oscar Peralta, Jorge Yslas

We introduce a class of continuous-time bivariate phase-type distributions for modeling dependencies from common shocks. The construction uses continuous-time Markov processes that…