Class schedule - Fall 2022

Date Description Slides  Homework
Wed. 8/31 Traveling to EUSIPCO 2022 - No class    
Mon. 9/5 Labor day - No class    
Wed. 9/7 Traveling to 2022 IEEE SPS/EURASIP Summer School - No class    
Mon. 9/12 Introductions, class organization, motivating example Block 1  
Wed. 9/14 Probability spaces, conditional probability, independence Block 2a  
Fri. 9/16 Random variables, discrete and continuous, expectations    
Mon. 9/19 Multiple RVs, joint distribution, expectations   HW1 due
Wed. 9/21 Bounds, convergence notions and limit theorems Block 2b  
Fri. 9/23 Conditional probabilities, distributions and expectations    
Mon. 9/26 Markov chains, examples, Chapman-Kolmogorov equations Block 3a HW2 due
Wed. 9/28 Gambler's ruin problem, discrete-time queuing models    
Mon. 10/3 Classes of states, irreducible Markov chains   HW3 due
Wed. 10/5 Limiting distributions Block 3b  
Mon. 10/10 Fall break - No class    
Wed. 10/12 Ergodicity   HW4 due
Mon. 10/17 Ranking of nodes in graphs Block 3c  
Wed. 10/19 Exponential times, memoryless property, counting processes Block 4a  
Mon. 10/24 Poisson processes, interarrival times, definitions, examples   HW5 due
Wed. 10/26 Continuous-time Markov chains, birth and death processes Block 4b  
Fri. 10/28 Midterm review lecture    
Mon. 10/31 Traveling to Asilomar 2022 - No class   HW6 due
Wed. 11/2 In-class midterm exam    
Mon. 11/7 Transition probability function, Kolmogorov's equations    
Wed. 11/9 Limiting distributions, ergodicity, balance equations   HW7 due
Fri. 11/11 Queuing theory, M/M/1, M/M/2, queue tandem Block 4c  
Mon. 11/14 Predator-prey population dynamics, Lotka-Volterra model Block 4d  
Wed. 11/16 Markov and Gaussian processes Block 5a  
Mon. 11/21 Brownian motion, geometric Brownian motion, white noise    
Wed. 11/23 Thanksgiving recess - No class   HW8 due
Mon. 11/28 Arbitrages and risk neutral measure Block 5b  
Wed. 11/30 Black-Scholes formula for options pricing    
Mon. 12/5 Stationary processes, implications, wide-sense stationarity Block 5c HW9 due
Wed. 12/7 Linear filtering of wide-sense stationary processes    
Mon. 12/12 Matched filter, Wiener filter    
Wed. 12/14 Principal component analysis   HW10 due