This second edition of the popular textbook contains a comprehensive course in modern probability theory. It includes a wealth of examples and more than 270 exercises as well as biographic details of key mathematicians.

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

Autorentext

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

Inhalt
Basic Measure Theory.- Independence.- Generating Functions.- The Integral.- Moments and Laws of Large Numbers.- Convergence Theorems.- Lp-Spaces and the RadonNikodym Theorem.- Conditional Expectations.- Martingales.- Optional Sampling Theorems.- Martingale Convergence Theorems and Their Applications.- Backwards Martingales and Exchangeability.- Convergence of Measures.- Probability Measures on Product Spaces.- Characteristic Functions and the Central Limit Theorem.- Infinitely Divisible Distributions.- Markov Chains.- Convergence of Markov Chains.- Markov Chains and Electrical Networks.- Ergodic Theory.- Brownian Motion.- Law of the Iterated Logarithm.- Large Deviations.- The Poisson Point Process.- The Ito Integral.- Stochastic Differential Equations.