Chapters 1-3
Results from these chapters that we refer to in later chapters are assumed to be known
Chapter 4
4.1
4.2
4.3. excluding the last part of 4.3 starting with the random-walk in 2 dimensions, i.e., the last part of Example 4.19.
4.4. excluding Examples 4.26, 4.27 and 4.28
4.5.1. The gambler's ruin problem
4.6. Mean time spent in transient states
4.7. Branching processes
4.8. Time reversible Markov Chains, excluding Example 4.39
4.9. Markov Chain Monte Carlo Methods, until Example 4.41
Chapter 5
5.1
5.2. The exponential distribution, excluding Examples 5.1, 5.5, 5.7, 5.9, 5.10 and 5.11
5.3. The Poisson Process. Excluding Examples 5.16, 5.17, the rest of 5.3.3, Proposition 5.6, Examples 5.18, 5.19, 5.20, 5.21 and 5.22 and Subsection 5.3.5
5.4. Generalizations of the Poisson process. Excluding Subsection 5.4.3
Chapter 6
6.1
6.2. Continuous-time Markov Chains
6.3. Birth and death processes, excluding the rest after Example 6.7
6.4. The transition probability function Pij(t), excluding Example 6.9 with remarks
6.5. Limiting probabilities, excluding Example 6.16
6.8. Uniformization
6.9. Computing the transition probabilities
Chapter 7
7.1. Introduction
7.2. Distribution of N(t)
Chapter 10
10.1. Brownian motion
10.2. Hitting times, maximum variable, and the gambler's ruin problem
10.3. Variations on Brownian motion