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20232026
most citedModeling discrete common-shock risks through matrix distributions

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math.PR2026

Least-Variable Harmonic Matrix-Exponential Distributions

Maria Laura Battagliola, Oscar Peralta

Concentrated matrix-exponential (CME) distributions are random clocks approximating a fixed time, with quality measured by the squared coefficient of variation (SCV); a well-known…

math.PR2026

Least Variability in a Polynomial-Square Class of Rational Kernels

Maria Laura Battagliola, Oscar Peralta

We solve an extremal problem for positive randomization kernels that concentrate a random time as tightly as possible around a deterministic target, within the class obtained by ex…

math.PR2026

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,…

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 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 ap…

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 and and an initial row vector , with strictly positive joint densities and a u…