Textbook
Sheldon M. Ross: "Introduction to Probability Models", 12th edition (2019), Academic Press, ISBN: 978-0-12-814346-9
Tentative Curriculum
- 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, until Example 4.37
- 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