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The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the gambler¿s ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright ¿Fisher model, Kingman¿s coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and Matlab¿.
The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the gambler¿s ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright ¿Fisher model, Kingman¿s coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and Matlab¿.
Contains 175 exercises including research-oriented problems about special stochastic processes not covered in traditional textbooks
Includes detailed simulation programs of the main models
Covers topics not typically included in traditional textbooks, allowing for readers to learn quickly on many topics, including research-oriented topics
Includes a timeline with the main contributors since the origin of probability theory until today
Includes supplementary material: [...]
Request lecturer material: [...]
| Erscheinungsjahr: | 2017 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Universitext |
| Inhalt: |
xiii
303 S. 57 s/w Illustr. 6 farbige Illustr. 303 p. 63 illus. 6 illus. in color. |
| ISBN-13: | 9783319500379 |
| ISBN-10: | 3319500376 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-50037-9 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Lanchier, Nicolas |
| Auflage: | 1st ed. 2017 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Universitext |
| Maße: | 235 x 155 x 18 mm |
| Von/Mit: | Nicolas Lanchier |
| Erscheinungsdatum: | 09.02.2017 |
| Gewicht: | 0,487 kg |
Contains 175 exercises including research-oriented problems about special stochastic processes not covered in traditional textbooks
Includes detailed simulation programs of the main models
Covers topics not typically included in traditional textbooks, allowing for readers to learn quickly on many topics, including research-oriented topics
Includes a timeline with the main contributors since the origin of probability theory until today
Includes supplementary material: [...]
Request lecturer material: [...]
| Erscheinungsjahr: | 2017 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Universitext |
| Inhalt: |
xiii
303 S. 57 s/w Illustr. 6 farbige Illustr. 303 p. 63 illus. 6 illus. in color. |
| ISBN-13: | 9783319500379 |
| ISBN-10: | 3319500376 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-50037-9 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Lanchier, Nicolas |
| Auflage: | 1st ed. 2017 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Universitext |
| Maße: | 235 x 155 x 18 mm |
| Von/Mit: | Nicolas Lanchier |
| Erscheinungsdatum: | 09.02.2017 |
| Gewicht: | 0,487 kg |
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