ECE 534: Random Processes (Fall 2022)

Course Information

Homework

Submissions via gradescope

Past Webpages

Spring 2020

Notes

Lectures are heavily based on the notes by Prof. Srikant and the text by Prof. Hajek (Spring 2020 syllabus).

For in-class notes, please contact Yixuan.

Disclaimer: The in-class notes correspond to files shared by your classmates. Therefore, no correction of typos or of technical

parts will be performed. It is highly suggested that you attend lectures, take your own notes and use the posted in-class notes as

complementary material.

Lectures

Week 1 Probability Space Reading: Lecture 1 by Prof. Srikant, Section 1.1 by Prof. Hajek
Week 2 Conditional Probability and Independence, Random Variables, Measurability and Lebesgue Integration Reading: Lectures 2,3 by Prof. Srikant, Sections 1.2, 1.3, 1.5 by Prof. Hajek
Week 3 Basic Inequalities (Markov, Reverse Markov and Chebyshev), Fundamental Functions (Characteristic, Moment Generating and Probability Generating), Important Distributions (Part 1) Reading: Lectures 3,4 by Prof. Srikant, Sections 1.5, 1.6 by Prof. Hajek
Week 4 Important Distributions (Part 2), Jointly Distributed Random Variables, Functions of Random Variables, Jensen's Inequality (Part 1) Reading: Lectures 4-7 by Prof. Srikant, Sections 1.6, 1.8-1.11, 2.4 by Prof. Hajek
Week 5 Jensen's Inequality (Part 2), Gaussian Tail and Chernoff Bounds, CLT, Hoeffding Bound (Part 1) Reading: Lectures 7-9 by Prof. Srikant, Sections 2.3-2.5 by Prof. Hajek
Week 6 Hoeffding Bound (Part 2), Change of Measure, Convergence of Sequences of Random Variables (Part 1) Reading: Lecture 11 by Prof. Srikant, Sections 2.1 by Prof. Hajek
Week 7 Convergence of Sequences of Random Variables (Part 2), Cauchy Criteria, Skorokhod's Representation Theorem, LLN (ms and WLLN), Borel-Cantelli Lemma ('The First Borell – Carntelli Lemma'), Monotone Covnergence Theorem Reading: Lecture 10 by Prof. Srikant, Sections 1.2, 2.2 by Prof. Hajek
Week 8 SLLN, MMSE and LMMSE Estimation Reading: Lecture 12 by Prof. Srikant, Sections 3.1-3.3 by Prof. Hajek
Week 9 Jointly Gaussian Random Variables Reading: Lecture 13 by Prof. Srikant, Section 3.4 by Prof. Hajek
Week 10 DTMCs Reading: Lecture 14 by Prof. Srikant, Sections 6.1-6.2 by Prof. Hajek
Week 11 Martingales, Poisson Process Reading: Lectures 17-18 by Prof. Srikant, Sections 4.3, 4.5 by Prof. Hajek
Week 12 Brownian Motion, Stationarity, Ergodicity, WSS, PSD Reading: Lectures 18,20,21,23,24,25 by Prof. Srikant, Sections 4.4, 4.6, 4.7, 7.4, 8.1-8.3 by Prof. Hajek
Weeks 13-14 Wiener and Kalman Filtering, Random Walks, Azuma-Hoeffding and McDiarmid's Inequalities. Also, Elements of Measure Theory (if time allows) Reading: Lectures 17, 22, 26 by Prof. Srikant, Sections 3.5, 3.6, 9.1, 9.5, 10.3 by Prof. Hajek

Exams

Midterm 1 Nov 3 in class
Midterm 2 Dec 1 in class
Final Dec 9, 1:30-4:30pm 3101 Sidney Lu Mech Engr Bldg