| 1 |
Probability Basics: Probability Space, σ-algebras, Probability Measure (PDF) |
| 2 |
Random Variables and Measurable Functions; Strong Law of Large Numbers (SLLN) (PDF) |
| 3 |
Large Deviations for i.i.d. Random Variables (PDF) |
| 4 |
Large Deviations Theory (cont.) (Part 1) (PDF)
Properties of the Distribution Function G (Part 2) (PDF) |
| 5 |
Brownian Motion; Introduction (PDF) |
| 6 |
The Reflection Principle; The Distribution of the Maximum; Brownian Motion with Drift (PDF) |
| 7 |
Quadratic Variation Property of Brownian Motion (PDF) |
| 8 |
Modes of Convergence and Convergence Theorems (PDF) |
| 9 |
Conditional Expectations, Filtration and Martingales (PDF) |
| 10 |
Martingales and Stopping Times (PDF) |
| 11 |
Martingales and Stopping Times (cont.); Applications (PDF) |
| 12 |
Introduction to Ito Calculus (PDF) |
| 13 |
Ito Integral; Properties (PDF) |
| 14 |
Ito Process; Ito Formula (PDF) |
| 15 |
Martingale Property of Ito Integral and Girsanov Theorem (PDF) |
| 16 |
Applications of Ito Calculus to Finance (PDF) |
| 17 |
Equivalent Martingale Measures (PDF) |
| 18 |
Probability on Metric Spaces (PDF) |
| 19 |
σ-fields on Measure Spaces and Weak Convergence (PDF) |
| 20 |
Functional Strong Law of Large Numbers and Functional Central Limit Theorem (PDF) |
| 21 |
G/G/1 Queueing Systems and Reflected Brownian Motion (RBM) (PDF) |
| 22 |
Fluid Model of a G/G/1 Queueing System (PDF) |
| 23 |
Fluid Model of a G/G/1 Queueing System (cont.) (PDF) |
| 24 |
G/G/1 in Heavy-traffic; Introduction to Queueing Networks (PDF) |
| 25 |
Final Notes and Ongoing Research Questions and Resources (PDF) |