Overview
- Comprehensive and modern introduction to the most important fields of probability theory
- Unique selection of topics, including many not usually found in introductory texts
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (26 chapters)
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Front Matter
Keywords
About this book
Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It 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)
Authors and Affiliations
Bibliographic Information
Book Title: Probability Theory
Book Subtitle: A Comprehensive Course
Authors: Achim Klenke
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-84800-048-3
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2008
eBook ISBN: 978-1-84800-048-3Published: 31 December 2007
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
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: Probability Theory and Stochastic Processes, Statistical Theory and Methods, Complex Systems, Statistical Physics and Dynamical Systems