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The exposition covers both the discrete time case, which is in principle relatively simple and allows step-by-step considerations, and the continuous-time case, which often requires more technical machinery such as martingales, supermartingales, and stochastic integrals. There is a focus on the well-developed apparatus of Brownian motion, which enables the exact solution of many problems. The last chapter presents applications to financial markets.
Researchers and graduate students interested in probability, decision theory and statistical sequential analysis will find this book useful.
The exposition covers both the discrete time case, which is in principle relatively simple and allows step-by-step considerations, and the continuous-time case, which often requires more technical machinery such as martingales, supermartingales, and stochastic integrals. There is a focus on the well-developed apparatus of Brownian motion, which enables the exact solution of many problems. The last chapter presents applications to financial markets.
Researchers and graduate students interested in probability, decision theory and statistical sequential analysis will find this book useful.
Albert N. Shiryaev is Chief Scientific Researcher and Professor of Probability Theory and Mathematical Statistics at the Steklov Mathematical Institute of the Russian Academy of Sciences and Head of the Department of Probability Theory in the Mechanics and Mathematics Faculty at Lomonosov Moscow State University. He is the author of several books, including Problems in Probability [translated by Andrew Lyasov], Optimal Stopping Rules [translated by A.B. Aries], and Statistics of Random Processes [with Robert S. Liptser]. He was the recipient of the A.A.MarkovPrize in 1974, of the A.N.Kolmogorov Prize in 1994, and of the Golden P.L.Chebyshev Medal of the Russian Academy of Science in 2017.
Provides the theory and methods to solve stochastic quickest detection tasks in disorder problems
Shows that most quickest detection problems can be reformulated as optimal stopping problems
Examines both the discrete-time and continuous-time cases
Preface.- Introduction.- Probabilistic-Statistical Models in Quickest Detection Problems. Discrete and Continuous Time.- Basic Settings and Solutions of Quickest Detection Problems. Discrete Time.- Optimal Stopping Times. General Theory for the Discrete-Time Case.- Optimal Stopping Rules. General Theory for the Discrete-Time Case in the Markov Representation.- Optimal Stopping Rules. General Theory for the Continuous-Time Case.- Basic Formulations and Solutions of Quickest Detection Problems. Continuous-Time. Models with Brownian motion.- Multi-Stage Quickest Detection of Breakdown of a Stationary Regime. Model with Brownian Motion.- Disorder on Filtered Probability Spaces.- Bayesian and Variational Problems of Hypothesis Testing. Brownian Motion Models.- Applications to Financial Mathematics.- References.- Term Index.- Notation Index.
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Reihe: | Probability Theory and Stochastic Modelling |
| Inhalt: |
xix
397 S. 27 s/w Illustr. 397 p. 27 illus. |
| ISBN-13: | 9783030015251 |
| ISBN-10: | 3030015254 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-030-01525-1 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Shiryaev, Albert N. |
| Übersetzung: | Iacob, Andrei |
| Auflage: | 1st ed. 2019 |
| Hersteller: |
Springer International Publishing
Probability Theory and Stochastic Modelling |
| Maße: | 241 x 160 x 29 mm |
| Von/Mit: | Albert N. Shiryaev |
| Erscheinungsdatum: | 20.03.2019 |
| Gewicht: | 0,793 kg |
Albert N. Shiryaev is Chief Scientific Researcher and Professor of Probability Theory and Mathematical Statistics at the Steklov Mathematical Institute of the Russian Academy of Sciences and Head of the Department of Probability Theory in the Mechanics and Mathematics Faculty at Lomonosov Moscow State University. He is the author of several books, including Problems in Probability [translated by Andrew Lyasov], Optimal Stopping Rules [translated by A.B. Aries], and Statistics of Random Processes [with Robert S. Liptser]. He was the recipient of the A.A.MarkovPrize in 1974, of the A.N.Kolmogorov Prize in 1994, and of the Golden P.L.Chebyshev Medal of the Russian Academy of Science in 2017.
Provides the theory and methods to solve stochastic quickest detection tasks in disorder problems
Shows that most quickest detection problems can be reformulated as optimal stopping problems
Examines both the discrete-time and continuous-time cases
Preface.- Introduction.- Probabilistic-Statistical Models in Quickest Detection Problems. Discrete and Continuous Time.- Basic Settings and Solutions of Quickest Detection Problems. Discrete Time.- Optimal Stopping Times. General Theory for the Discrete-Time Case.- Optimal Stopping Rules. General Theory for the Discrete-Time Case in the Markov Representation.- Optimal Stopping Rules. General Theory for the Continuous-Time Case.- Basic Formulations and Solutions of Quickest Detection Problems. Continuous-Time. Models with Brownian motion.- Multi-Stage Quickest Detection of Breakdown of a Stationary Regime. Model with Brownian Motion.- Disorder on Filtered Probability Spaces.- Bayesian and Variational Problems of Hypothesis Testing. Brownian Motion Models.- Applications to Financial Mathematics.- References.- Term Index.- Notation Index.
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Reihe: | Probability Theory and Stochastic Modelling |
| Inhalt: |
xix
397 S. 27 s/w Illustr. 397 p. 27 illus. |
| ISBN-13: | 9783030015251 |
| ISBN-10: | 3030015254 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-030-01525-1 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Shiryaev, Albert N. |
| Übersetzung: | Iacob, Andrei |
| Auflage: | 1st ed. 2019 |
| Hersteller: |
Springer International Publishing
Probability Theory and Stochastic Modelling |
| Maße: | 241 x 160 x 29 mm |
| Von/Mit: | Albert N. Shiryaev |
| Erscheinungsdatum: | 20.03.2019 |
| Gewicht: | 0,793 kg |
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