RT Journal Article
T1 On first-passage times and sojourn times in finite qbd processes and their applications in epidemics
A1 Gómez Corral, Antonio
A1 López-García, M.
A1 López Herrero, María Jesús
A1 Taipe Hidalgo, Diana Paulina
AB In this paper, we revisit level-dependent quasi-birth-death processes with finitely many possible values of the level and phase variables by complementing the work of Gaver, Jacobs, and Latouche (Adv. Appl. Probab. 1984), where the emphasis is upon obtaining numerical methods for evaluating stationary probabilities and moments of first-passage times to higher and lower levels. We provide a matrix-analytic scheme for numerically computing hitting probabilities, the number of upcrossings, sojourn time analysis, and the random area under the level trajectory. Our algorithmic solution is inspired from Gaussian elimination, which is applicable in all our descriptors since the underlying rate matrices have a block-structured form. Using the results obtained, numerical examples are given in the context of varicella-zoster virus infections.
PB MDPI
SN 2227-7390
YR 2020
FD 2020-10
LK https://hdl.handle.net/20.500.14352/102080
UL https://hdl.handle.net/20.500.14352/102080
LA eng
NO Gómez-Corral, A. et al. (2020) «On first-passage times and sojourn times in finite qbd processes and their applications in epidemics», Mathematics, 8(10), pp. 1-26. doi:10.3390/MATH8101718.
DS Docta Complutense
RD 18 abr 2025