Random Processes in Systems
Week 1
- Jan 16
- Probability Spaces; Kolmogorov Axioms; Consequences
- 1.1, App. A
- Jan 17
- Section Discussion 1
- Jan 18
- Borel-Cantelli; Existence/Uniqueness of Probability; Random Variables
- 1.2.1-1.2.4; review 1.2.7 on your own
- Jan 21
- HW 1 due
Week 2
- Jan 23
- Random Variables; Joint Distributions; Independence
- 1.2.3-1.2.4
- Jan 24
- Section Discussion 2
- Jan 25
- Expectation; Fatou’s Lemma; Monotone and Dominated Convergence Theorems
- 1.2.5-1.2.6
Week 3
- Jan 29
- HW 2 due
- Jan 30
- No Lecture
- Jan 31
- Section Discussion 3
- Feb 1
- Conditional Probability
- 1.3
Week 4
- Feb 5
- HW 3 due
- Feb 6
- Limit Theorems; Stochastic Processes
- 1.5, 2.1-2.2
- Feb 7
- Section Discussion 4
- Feb 8
- Strong Law of Large Numbers
- 2.1-2.2
Week 5
- Feb 12
- HW 4 due
- Feb 13
- Modes of Convergence; Central Limit Theorem
- 2.3.1-2.3.2
- Feb 14
- Section Discussion 5
- Feb 15
- Gaussian Vectors; Central Limit Theorem
- 2.3.1-2.3.2, Ch. 3
Week 6
- Feb 19
- HW 5 due
- Feb 20
- Gaussian Processes; Central Limit Theorem
- 2.3.1-2.3.2, Ch. 3
- Feb 21
- Section Discussion 6
- Feb 22
- Linear Estimation; Hilbert Space; Best Linear Estimator
- App. B; 4.1-4.2
Week 7
- Feb 26
- HW 6 due
- Feb 27
- More on Linear Estimation; Linear Innovations; Kalman Filter
- 4.3-4.5
- Feb 28
- Section Discussion 7
- Feb 29
- No Lecture
Week 8
- Mar 5
- Midterm
- Second-order Processes; Spectral Theory; Wide Sense Stationarity
- 5.1-5.3; App. C
- Mar 6
- Section Discussion 8
- Mar 7
- Optimal Filtering of WSS Processes
- 5.4-5.5
Week 9
- Mar 11
- HW 8 due
- Mar 12
- No Lecture
- Mar 13
- Section Discussion 9
- Mar 14
- WSS Signals and LTI Systems
- 5.5
Week 10
- Mar 18
- HW 9 due
- Mar 19
- Discrete-Time Markov Chains; Chapman-Kolmogorov Equations; Classification of States
- 6.1
- Mar 20
- Section Discussion 10
- Mar 21
- Discrete-Time Markov Limit Theorems
- 6.2
Week 11
Spring Break!
Week 12
- Apr 1
- HW 10 due
- Apr 2
- Reversibility; Spectral Gap
- 6.3
- Apr 3
- Section Discussion 11
- Apr 4
- Martingales - Definitions and Examples
- 7.1
Week 13
- Apr 8
- HW 11 due
- Apr 9
- Stopping Times; Optional Stopping Theorem
- 7.2
- Apr 10
- Section Discussion 12
- Apr 11
- Concentration Inequalities; Martingale Convergence Theorem
- 7.3-7.4
Week 14
- Apr 15
- HW 12 due
- Apr 16
- Poisson Processes - Definitions and Properties
- Ch. 8
- Apr 17
- Section Discussion 13
- Apr 18
- Continuous-Time Markov Chains; Kolmogorov Differential Equations; Classifcation of States
- 9.1-9.2
Week 15
- Apr 22
- HW 13 due
- Apr 23
- Continuous-Time Markov Limit Theorems
- 9.3
- Apr 24
- Section Discussion 14
- Apr 25
- Reversibility and Spectral Gap
- 9.4