Probability: Theory and Examples
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The new edition begins with a short chapter on measure theory to orient readers new to the subject.
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Review: Probability: Theory and ExamplesUser Review - Xing Shi - Goodreads
I like the book because it usually gives proof for theorems in more generalized forms, but I really don't like the typos in the electronic version. I'm not sure about the printed version, but if it's the same the electronic one, then an errata is definitely needed. Read full review