|
Topic |
Durrett |
Pinsky-Karlin |
Dobrow |
1 |
The exponential distribution |
2.1 |
1.4.2, 1.5.2 |
N/A |
2 |
Birth and death processes |
N/A |
6.1-6.3 |
N/A |
3 |
General continuous-time Markov chains |
4.1 |
6.6 |
7.1-7.2 |
4 |
First-jump conditioning and hitting probabilities |
4.4 |
6.5 |
N/A |
5 |
Kolmogorov's forward and backward equations |
4.2 |
6.3.3, 6.6 |
7.3 |
6 |
Stationary distributions and long-run behavior |
4.3 |
6.4 |
7.4 |
7 |
Introduction to renewal processes |
3.1 |
7.1-7.3 |
N/A |
8 |
Asymptotic results for renewal processes |
3.1 |
7.4 |
N/A |
9 |
Renewal reward processes |
3.1 |
7.5 |
N/A |
10 |
Age and residual life |
3.3 |
N/A |
N/A |
11 |
The M/M/1 queue |
4.5.1 |
9.1-9.2 |
7.6 |
12 |
Other queues with exponential service times |
4.5.2 |
9.2 |
7.6 |
13 |
Queues with general service times |
3.2 |
9.3 |
N/A |
14 |
Queues in tandem |
4.6 |
9.5 |
N/A |
15 |
Definition and basic properties of Brownian motion |
N/A |
8.1 |
8.1-8.2 |
16 |
Brownian motion as a Gaussian process |
N/A |
8.1 |
8.3 |
17 |
The reflection principle |
N/A |
8.2 |
8.4 |
18 |
Zeros of Brownian motion |
N/A |
8.2 |
8.4 |
19 |
Brownian motion with drift |
N/A |
8.4 |
8.5 |
20 |
Geometric Brownian motion |
N/A |
8.4 |
8.5 |
21 |
Other processes derived from Brownian motion |
N/A |
8.3 |
8.5 |