## Overview

- 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

Part of the book series: Universitext (UTX)

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## About this book

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.

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.

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## Table of contents (26 chapters)

## Authors and Affiliations

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## Bibliographic Information

Book Title: Probability Theory

Book Subtitle: A Comprehensive Course

Authors: Achim Klenke

Series Title: Universitext

DOI: https://doi.org/10.1007/978-3-030-56402-5

Publisher: Springer Cham

eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Softcover ISBN: 978-3-030-56401-8Published: 31 October 2020

eBook ISBN: 978-3-030-56402-5Published: 30 October 2020

Series ISSN: 0172-5939

Series E-ISSN: 2191-6675

Edition Number: 3

Number of Pages: XIV, 716

Number of Illustrations: 31 b/w illustrations, 24 illustrations in colour

Topics: Probability Theory and Stochastic Processes, Measure and Integration, Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Theoretical, Mathematical and Computational Physics