Save 40% on select Business & Management books + FREE shipping or 50% on Physics eBooks!

Universitext

Probability Theory

A Comprehensive Course

Authors: Klenke, Achim

Free Preview
  • Comprehensive and modern introduction to the most important fields of probability theory
  • Unique selection of topics, including many not usually found in introductory texts
  • Plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation
see more benefits

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-1-84800-048-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
About this Textbook

Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils of random developments on the financial markets, and they guide us in constructing more efficient algorithms.

This text is a comprehensive course in modern probability theory and its measure-theoretical foundations. Aimed primarily at graduate students and researchers, the book covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as:

  • limit theorems for sums of random variables;
  • martingales;
  • percolation;
  • Markov chains and electrical networks;
  • construction of stochastic processes;
  • Poisson point processes and infinite divisibility;
  • large deviation principles and statistical physics;
  • Brownian motion; and
  • 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 the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.

Reviews

From the reviews:

"The book is indeed comprehensive, consisting of 26 chapters on different topics. … can be well used as a reference book on a wide range of topics. The target audience is researchers and graduate students … . Numerous advanced topics are included, so that the book is more inclusive … . There is more than enough material for a two-semester course here. … the book will primarily be used as a reference book. For that purpose, it is a rich and relatively inexpensive choice." (Miklós Bóna, MathDL, January, 2008)

"This book of over 600 pages gives a self-contained presentation of modern probability theory. It is based on courses on advanced probability given by the author. … Most of the proofs are well detailed. … This book will be helpful for graduate students in mathematics … and for researchers in mathematics or theoretical physics." (Sophie Lemaire, Mathematical Reviews, Issue 2009 f)


Table of contents (26 chapters)

Table of contents (26 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-1-84800-048-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Probability Theory
Book Subtitle
A Comprehensive Course
Authors
Series Title
Universitext
Copyright
2008
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84800-048-3
DOI
10.1007/978-1-84800-048-3
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XII, 621
Number of Illustrations
23 b/w illustrations
Additional Information
Original German edition published by Springer Verlag Berlin Heidelberg, 2006
Topics