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Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as:
limit theorems for sums of random variables
martingales
percolation
Markov chains and electrical networks
construction of stochastic processes
Poisson point process and infinite divisibility
large deviation principles and statistical physics
Brownian motion
stochastic integrals and stochastic differential equations.
The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts.
This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.
Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as:
limit theorems for sums of random variables
martingales
percolation
Markov chains and electrical networks
construction of stochastic processes
Poisson point process and infinite divisibility
large deviation principles and statistical physics
Brownian motion
stochastic integrals and stochastic differential equations.
The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts.
This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.
Provides a complete introduction to probability theory, including measure theory and scientific applications
New updated edition includes concise summaries of each section, as well as outlooks and questions in the text
Clearly written to make complicated mathematics accessible
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 732 |
| Reihe: | Universitext |
| Inhalt: |
xiv
716 S. 31 s/w Illustr. 24 farbige Illustr. 716 p. 55 illus. 24 illus. in color. |
| ISBN-13: | 9783030564018 |
| ISBN-10: | 3030564010 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Klenke, Achim |
| Auflage: | 3rd ed. 2020 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Universitext |
| Maße: | 235 x 155 x 40 mm |
| Von/Mit: | Achim Klenke |
| Erscheinungsdatum: | 31.10.2020 |
| Gewicht: | 1,089 kg |
Provides a complete introduction to probability theory, including measure theory and scientific applications
New updated edition includes concise summaries of each section, as well as outlooks and questions in the text
Clearly written to make complicated mathematics accessible
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 732 |
| Reihe: | Universitext |
| Inhalt: |
xiv
716 S. 31 s/w Illustr. 24 farbige Illustr. 716 p. 55 illus. 24 illus. in color. |
| ISBN-13: | 9783030564018 |
| ISBN-10: | 3030564010 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Klenke, Achim |
| Auflage: | 3rd ed. 2020 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Universitext |
| Maße: | 235 x 155 x 40 mm |
| Von/Mit: | Achim Klenke |
| Erscheinungsdatum: | 31.10.2020 |
| Gewicht: | 1,089 kg |
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