Probability Theory

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.

• Probability theory
• Random variable
• common limit theorems
• measure theory
• modern probability theory
• probability
• statistical physics
• stochastic processes

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)

• Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Mainz, Germany

  Achim Klenke

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