This book is an introduction to probability theory include the law of large numbers, Central limit theorems, random walks, martingales, Markov chain, ergodic theorems, and motion. It is a holistic treatment focus on the results that are most useful for applications. Its philosophy is the best way to learn is to see it in action, so for example 200 and 450 problem.
Table of Contents
1. Measure theory 2. Laws of large numbers 3. Central limit theorems 4. Random walks 5. Martingales 6. Markov chains 7. Ergodic theorems 8. Brownian motion Appendix A. Measure theory details.
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