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