This popular textbook, now in a revised and expanded third edition,
presents a comprehensive course in modern probability theory.
Probability plays an increasingly important role not only in
mathematics, but also in physics, biology, finance and computer science,
helping to understand phenomena such as magnetism, genetic diversity and
market volatility, and also to construct efficient algorithms. Starting
with the very basics, this textbook covers a wide variety of topics in
probability, including many not usually found in introductory books,
such as:
- 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 integrals and stochastic differential equations.
The presentation is self-contained and mathematically rigorous, with the
material on probability theory interspersed with chapters on measure
theory to better illustrate the power of abstract concepts.
This third edition has been carefully extended and includes new
features, such as concise summaries at the end of each section and
additional questions to encourage self-reflection, as well as updates to
the figures and computer simulations. With a wealth of examples and more
than 290 exercises, as well as biographical details of key
mathematicians, it will be of use to students and researchers in
mathematics, statistics, physics, computer science, economics and
biology.
