RT Journal Article
T1 A computational approach to extreme values and related hitting probabililties in level-dependent quasi-birth-death processes
A1 Crescenzo, Antonio di
A1 Gómez Corral, Antonio
A1 Taipe Hidalgo, Diana Paulina
AB This paper analyzes the dynamics of a level-dependent quasi-birth-death process X = {(I(t), J(t)) : t ≥ 0}, i.e., a bi-variate Markov chain defined on the countable state space ∪∞ i=0l(i) with l(i) = {(i, j) : j ∈ {0, ..., Mi}}, for integers Mi ∈ N0 and i ∈ N0, which has the special property that its q-matrix has a block-tridiagonal form. Under the assumption that the first passage to the subset l(0) occurs in a finite time with certainty, we characterize the probability law of (τmax, Imax, J(τmax)), where Imax is the running maximum level attained by process X before its first visit to states in l(0), τmax is the first time that the level process {I(t) : t ≥ 0} reaches the running maximum Imax, and J(τmax) is the phase at time τmax. Our methods rely on the use of restricted LaplaceStieltjes transforms of τmax on the set of sample paths {Imax = i, J(τmax) = j}, and related processes under taboo of certain subsets of states. The utility of the resulting computational algorithms is demonstrated in two epidemic models: the SIS model for horizontally and vertically transmitted diseases; and the SIR model with constant population size.
PB Elsevier
YR 2024
FD 2024
LK https://hdl.handle.net/20.500.14352/108004
UL https://hdl.handle.net/20.500.14352/108004
LA eng
NO Di Crescenzo A, Gómez-Corral A, Taipe D. A computational approach to extreme values and related hitting probabilities in level-dependent quasi-birth–death processes, Mathematics and Computers in Simulation, 2024.
NO 2023 Acuerdos transformativos CRUE
NO Ministerio de Ciencia e Innovación
NO Banco Santander - Universidad Complutense de Madrid
DS Docta Complutense
RD 27 abr 2025