Universitext

Probability Theory

A Comprehensive Course

Authors: Klenke, Achim

  • 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
see more benefits

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4471-5361-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-1-4471-5360-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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.

About the authors

Achim Klenke is a professor at the Johannes Gutenberg University in Mainz, Germany. 

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)


Table of contents (26 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4471-5361-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-1-4471-5360-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Probability Theory
Book Subtitle
A Comprehensive Course
Authors
Series Title
Universitext
Copyright
2014
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-1-4471-5361-0
DOI
10.1007/978-1-4471-5361-0
Softcover ISBN
978-1-4471-5360-3
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XII, 638
Number of Illustrations and Tables
26 b/w illustrations, 20 illustrations in colour
Topics