## Overview

- Presents an updated, comprehensive and modern introduction to the most important fields of probability theory
- Contains many new figures and examples
- Studies a wide variety of topics on probability theory, many of which are not found in introductory textbooks
- Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

## Access this book

Tax calculation will be finalised at checkout

## Other ways to access

## About this book

This second edition of the popular textbook contains a comprehensive course in modern probability theory, covering a wide variety of topics which are not usually found in introductory textbooks, including:

• 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 integral and stochastic differential equations.

The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.

### Similar content being viewed by others

## Keywords

## Table of contents (26 chapters)

## Reviews

From the book reviews:

“The book is dedicated to graduate students who start to learn probability theory as well as to those who need an excellent reference book. … All results are presented in a self-contained way and are rigorously proved. Each section of the 26 chapters ends with a number of exercises, overall more than 270. … Altogether it is a very valuable book for all students who specialize in probability theory or statistics.” (Mathias Trabs, zbMATH, Vol. 1295, 2014)

“The book under review is a standard graduate textbook in this area of mathematics that collects various classical and modern topics in a friendly volume. … the book contains many exercises. It is a very good source for a course in probability theory for advanced undergraduates and first-year graduate students. … the book should be useful for a wide range of audiences, including students, instructors, and researchers from all branches of science who are dealing with random phenomena.” (Mehdi Hassani, MAA Reviews, May, 2014)

## Authors and Affiliations

## About the author

## Bibliographic Information

Book Title: Probability Theory

Book Subtitle: A Comprehensive Course

Authors: Achim Klenke

Series Title: Universitext

DOI: https://doi.org/10.1007/978-1-4471-5361-0

Publisher: Springer London

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

Copyright Information: Springer-Verlag London 2014

eBook ISBN: 978-1-4471-5361-0Published: 30 August 2013

Series ISSN: 0172-5939

Series E-ISSN: 2191-6675

Edition Number: 2

Number of Pages: XII, 638

Number of Illustrations: 26 b/w illustrations, 20 illustrations in colour

Topics: Probability Theory and Stochastic Processes, Measure and Integration, Dynamical Systems and Ergodic Theory, Functional Analysis, Complex Systems, Statistical Physics and Dynamical Systems