LD-QBD Processes with Applications in Epidemic Models
This thesis focuses on level-dependent quasi-birth-death (LD-QBD) processes, i.e., bivariate Markov chains X = {(I(t), J(t)) : t ≥ 0} defined on the state space S =∪∞i=0l(i), which is structured by levels l(i) = {(i, j) : j ∈ {0, ...,Mi}}, for Mi ∈ N0and i ∈ N0, so that the corresponding q-matrix ha...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/132442 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/132442 |
| Access Level: | acceso abierto |
| Palabra clave: | 004.6(043.2) Estadística 1209.03 Análisis de Datos |
| Sumario: | This thesis focuses on level-dependent quasi-birth-death (LD-QBD) processes, i.e., bivariate Markov chains X = {(I(t), J(t)) : t ≥ 0} defined on the state space S =∪∞i=0l(i), which is structured by levels l(i) = {(i, j) : j ∈ {0, ...,Mi}}, for Mi ∈ N0and i ∈ N0, so that the corresponding q-matrix has a block-tridiagonal form. In this context, our main interest is to study first-passage times and related hitting probabilities, sojourn times, and extreme values, under the taboo of certain sets of states and sample paths. We first consider the framework of finite QBD processes, where the state space S is restricted to ∪Ni=0l(i) with N ∈ N. In particular, we derive recursive expressions for the distribution and moments of first-passage times to higher levels l(K) and restricted hitting probabilities, as well as the number of jumps from states in level l(K − 1) tolevel l (K) before the first visit to level l(0)... |
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