Below you find a plan for the weekly lectures.
Please note that some parts of the chapters are skipped. You may have a look at the pensum for the precise content of the curriculum.
Week 3
- Monday 15 January:
- Ch. 2.9: Introduction to stochastic processes
- Start on Ch. 4.1: Introduction to Markov Chains
- Wednesday 17 January:
- Finish Ch. 4.1
- Start Ch. 4.2: Chapman-Kolmogorov Equations
You can find the lecture notes for this week here
Week 4
- Monday 22 January:
- Finish Ch. 4.2
- Wednesday 24 January:
- Ch. 4.3: Classification of States
You can find the lecture notes for this week here
Week 5
- Monday 29 January:
- Start Ch. 4.4: Long-Run Proportions and Limiting Probabilities
- Wednesday 31 January:
- Cont. Ch. 4.4
You can find the lecture notes for this week here
Week 6
- Monday 5 February:
- Finish Ch. 4.4
- Start Ch. 4.5.1: The Gambler's Ruin Problem
- Wednesday 7 February:
- Finish Ch. 4.5.1
- Ch. 4.6: Mean Time Spent in Transient States
You can find the lecture notes for this week here
Week 7
- Monday 12 February:
- Start Ch. 4.7: Branching Processes
- Wednesday 14 February:
- Finish Ch. 4.7
- Ch 4.8: Time Reversible Markov Chains
You can find the lecture notes for this week here
Week 8
- Monday 19 February:
- Start Ch. 4.9: Markov Chain Monte Carlo Methods
- Wednesday 21 February:
- Finish Ch. 4.9
- Ch. 5.1
- Start Ch. 5.2: The Exponential Distribution
You can find the lecture notes for this week here
Week 9
- Monday 26 February:
- Cont. Ch. 5.2
- Wednesday 28 February:
- Cont. Ch. 5.2
You can find the lecture notes for this week here
Week 10
- Monday 5 March:
- Finish Ch. 5.2
- Start Ch. 5.3: The Poisson process
- Wednesday 7 March:
- Cont. Ch. 5.3
You can find the lecture notes for this week here
Week 11
- Monday 12 March:
- Cont. Ch. 5.3
- Wednesday 14 March:
- Cont. Ch. 5.3
You can find the lecture notes for this week here
Week 14
- Wednesday 4 April:
- Finish Ch. 5.3
- Start Ch. 5.4 : Generalizations of the Poisson Process
You can find the lecture notes for this week here
Week 15
- Monday 9 April:
- Cont. Ch. 5.4
- Wednesday 11 April:
- Finish Ch. 5.4
- Ch. 6.1 and 6.2 : Continuous-Time Markov Chains
- Start Ch. 6.3: Birth and Death Processes
You can find the lecture notes for this week here
Week 16
- Monday 16 April:
- Cont. Ch. 6.3
- Wednesday 18 April:
- Finish Ch. 6.3
- Start Ch. 6.4: The Transition Probability Function Pi,j(t)
You can find the lecture notes for this week here
Week 17
- Monday 23 April:
- Cont. Ch. 6.4
- Wednesday 25 April:
- Finish Ch. 6.4
- Start Ch. 6.5: Limiting Probabilities
You can find the lecture notes for this week here
Week 18
- Monday 30 April:
- Finish Ch. 6.5
- Start Ch. 6.8 : Uniformization
- Wednesday 2 May:
- Finish Ch. 6.8
- Ch. 6.9: Computing the Transition Probabilities
- Ch. 7.1: Renewal Theory
- Start Ch. 7.2 Distribution of N(t)
You can find the lecture notes for this week here
Week 19
- Monday 7 May:
- Finish Ch. 7.2
- Start Ch. 10.1: Brownian Motion
- Wednesday 9 May:
- Finish Ch. 10.1
- Ch. 10.2: Hitting Times and the Maximum Variable
- Ch. 10.3: Variations of Brownian Motion
You can find the lecture notes for this week here