Statistical Inference for Piecewise-Deterministic Markov Processes.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Azais, Romain
Otros Autores: Bouguet, Florian
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2018.
Temas:
Markov processes.
Processus de Markov.
Markov processes
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover; Half-Title Page; Series Page; Title Page; Copyright Page; Contents; Preface; List of Acronyms; Introduction; 1. Statistical Analysis for Structured Models on Trees; 1.1. Introduction; 1.1.1. Motivation; 1.1.2. Genealogical versus temporal data; 1.2. Size-dependent division rate; 1.2.1. From partial differential equation to stochastic models; 1.2.2. Non-parametric estimation: the Markov tree approach; 1.2.3. Sketch of proof of Theorem 1.1; 1.3. Estimating the age-dependent division rate; 1.3.1. Heuristics and convergence of empirical measures; 1.3.2. Estimation results.
  • 1.3.3. Sketch of proof of Theorem 1.41.4. Bibliography; 2. Regularity of the Invariant Measure and Non-parametric Estimation of the Jump Rate; 2.1. Introduction; 2.2. Absolute continuity of the invariant measure; 2.2.1. The dynamics; 2.2.2. An associated Markov chain and its invariant measure; 2.2.3. Smoothness of the invariant density of a single particle; 2.2.4. Lebesgue density in dimension N; 2.3. Estimation of the spiking rate in systems of interacting neurons; 2.3.1. Harris recurrence; 2.3.2. Properties of the estimator; 2.3.3. Simulation results; 2.4. Bibliography.
  • 3. Level Crossings and Absorption of an Insurance Model3.1. An insurance model; 3.2. Some results about the crossing and absorption features; 3.2.1. Transition density of the post-jump locations; 3.2.2. Absorption time and probability; 3.2.3. Kac-Rice formula; 3.3. Inference for the absorption features of the process; 3.3.1. Semi-parametric framework; 3.3.2. Estimators and convergence results; 3.3.3. Numerical illustration; 3.4. Inference for the average number of crossings; 3.4.1. Estimation procedures; 3.4.2. Numerical application; 3.5. Some additional proofs; 3.5.1. Technical lemmas.
  • 3.5.2. Proof of Proposition 3.33.5.3. Proof of Corollary 3.2; 3.5.4. Proof of Theorem 3.5; 3.5.5. Proof of Theorem 3.6; 3.5.6. Discussion on the condition (CG2); 3.6. Bibliography; 4. Robust Estimation for Markov Chains with Applications to Piecewise-deterministic Markov Processes; 4.1. Introduction; 4.2. (Pseudo)-regenerative Markov chains; 4.2.1. General Harris Markov chains and the splitting technique; 4.2.2. Regenerative blocks for dominated families; 4.2.3. Construction of regeneration blocks; 4.3. Robust functional parameter estimation for Markov chains.
  • 4.3.1. The influence function on the torus4.3.2. Example 1: sample means; 4.3.3. Example 2: M-estimators; 4.3.4. Example 3: quantiles; 4.4. Central limit theorem for functionals of Markov chains and robustness; 4.5. A Markov view for estimators in PDMPs; 4.5.1. Example 1: Sparre Andersen model with barrier; 4.5.2. Example 2: kinetic dietary exposure model; 4.6. Robustness for risk PDMP models; 4.6.1. Stationary measure; 4.6.2. Ruin probability; 4.6.3. Extremal index; 4.6.4. Expected shortfall; 4.7. Simulations; 4.8. Bibliography.

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