Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model [recurso electrónico] / by Ingemar Nåsell.
Tipo de material: TextoSeries Lecture Notes in Mathematics ; 2022Editor: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011Descripción: XI, 199 p. 10 illus. in color. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642205309Tema(s): Mathematics | Life sciences | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic Processes | Life Sciences, generalFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 519.2 Clasificación LoC:QA273.A1-274.9QA274-274.9Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
---|---|---|---|---|---|---|---|
Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA273 .A1-274.9 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 376097-2001 |
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QA273 .A1-274.9 Risk and Meaning | QA273 .A1-274.9 Random Perturbation of PDEs and Fluid Dynamic Models | QA273 .A1-274.9 Markov Decision Processes with Applications to Finance | QA273 .A1-274.9 Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model | QA273 .A1-274.9 Disorder and Critical Phenomena Through Basic Probability Models | QA273 .A1-274.9 Markov Paths, Loops and Fields | QA273 .A1-274.9 Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems |
1 Introduction -- 2 Model Formulation -- 3 A Birth-Death Process with Finite State Space and with an Absorbing State at the Origin -- 4 The SIS Model: First Approximations of the Quasi-Stationary Distribution -- 5 Some Approximations Involving the Normal Distribution -- 6 Preparations for the Study of the Stationary Distribution p(1) of the SIS Model -- 7 Approximation of the Stationary Distribution p(1) of the SIS Model -- 8 Preparations for the Study of the Stationary Distribution p(0) of the SIS Model -- 9 Approximation of the Stationary Distribution p(0) of the SIS Model -- 10 Approximation of Some Images UnderY for the SIS Model -- 11 Approximation of the Quasi-Stationary Distribution q of the SIS Model -- 12 Approximation of the Time to Extinction for the SIS Model -- 13 Uniform Approximations for the SIS Model -- 14 Thresholds for the SIS Model -- 15 Concluding Comments.
This volume presents explicit approximations of the quasi-stationary distribution and of the expected time to extinction from the state one and from quasi-stationarity for the stochastic logistic SIS model. The approximations are derived separately in three different parameter regions, and then combined into a uniform approximation across all three regions. Subsequently, the results are used to derive thresholds as functions of the population size N.
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