• 1. Measure theory--
• 2. Laws of large numbers--
• 3. Central limit theorems--
• 4. Martingales--
• 5. Markov chains--
• 6. Ergodic theorems--
• 7. Brownian motion--
• 8. Applications to random walk--
• 9. Multidimensional Brownian motion-- Appendix. Measure theory details.
• (source: Nielsen Book Data)

This lively introduction to measure-theoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference. Operating under the philosophy that the best way to learn probability is to see it in action, the book contains extended examples that apply the theory to concrete applications. This fifth edition contains a new chapter on multidimensional Brownian motion and its relationship to partial differential equations (PDEs), an advanced topic that is finding new applications. Setting the foundation for this expansion, Chapter 7 now features a proof of Ito's formula. Key exercises that previously were simply proofs left to the reader have been directly inserted into the text as lemmas. The new edition re-instates discussion about the central limit theorem for martingales and stationary sequences.
(source: Nielsen Book Data)

• 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.
• (source: Nielsen Book Data)

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.
(source: Nielsen Book Data)