Elementary
Stochastic Processes
and Its Applications

★★★ 2022/08/15 ★★★

Main textbook has been decided; you can find a copy and read it in your summer vacation! Notice that we will follow school's schedule (16weeks + 2 extra support weeks). Check the following tentative schedule, where more details will be added later. I will try to present more applications (particularly with communications or signal processing) of each topic to engage your learning. 

Course Information

Instructor: Jian-Jia Weng

Time: 107, 108, 109 (Mon. 14:10-15:00, 15:00-16:00, 16:05-16:55)

Location: EE1-R103

Office and Office Hour: EE1-R404 Tue 10:00-12:00  (It is always better to make an appointment before coming!)

Material: the course will be delivered by slides or handwriting notes mainly based on the following textbook:

1. Henry Stark and John W. Woods, Probability and Random Processes with Applications to Signal Processing, 4th Ed.

Grading Policy: 4 Homework Assignments (60%), Mid-Term (15%), Final Exam (15%), Oral Presentation (10%)

Contact Information

Office: EE1-R404

Campus Internal Phone Number：6211

Email: jjweng AT email.ntou.edu.tw

If you have any questions regarding the course and cannot reach me during office hours, you can email me with 

• Subject: [ESPA 2022] Inquiry - Your name and Student ID number

• Contents: (1) topics you want to discuss and (2) your preferred time to meet in person (please specify at least 3 time slots). 

I should reply to your email within 24hours; if not, please send the email again.

Tentative Schedule

• Week 1 (09/12): 

  1. Review of Basic Probability [Chapter 1]

  2. Axiom Approach of Probability

  3. Sigma-Field

  4. Probability Measure

• Week 2  (09/19): 

  1. Random Variables [Chapter 2]

  2. Reliability Function and Failure Rate

  3. Functions of Random Variables [Chapter 3]

• Week 3 (09/26): 

  1. Expectations and Moments [Chapter 4]

  2. Random Vectors [Ch. 5]

• Week 4 (10/03): HW1 Due

  1. Parameter Estimation [Ch. 6]

  2. (Affine) Mean Square Error Estimator

  3. Maximum-a-Posteriori Estimator

  4. Gaussian Random Vectors

• Week 5 (10/10): No Class

• Week 6 (10/17): 

  1. Gaussian Random Vectors (Cont'd)

  2. Random Processes - General Definition

• Week 7 (10/24):

  1. Random Sequences [Ch. 8.1]

• Week 8 (10/31): Midterm Exam

  1. Random Sequences (Cont'd) [Ch. 8.1] 

• Week 9 (11/07): 

  1. Random Sequences (Cont'd) [Ch. 8.1-]

• Week 10 (11/14): HW2 Due

  1. Random Processes [Ch. 9]

• Week 11 (11/21):

  1. General Properties of Stochastic Processes

• Week 12 (11/28): 

  1. Stochastic Processes in Linear Systems

  2. Power Spectral Density

• Week 13 (12/05): HW3 Due

  1. Matched Filter and Wiener Filter

• Week 14 (12/12):

  1. Markov Processes

• Week 15 (12/19): 

  1. Markov Processes (Cont'd)

  2. Poisson Processes

• Week 16 (12/26): Final Exam

  1. Poisson Processes (Cont'd)

• Week 17 (01/02): No Class/HW4 Due

• Week 18 (01/09): Oral Presentation

Homework Assignments

• Homework 1:  (posted on 07:14 AM Oct. 13, due date: 11: 59 PM Oct. 09) 

• Homework 2: (posted on, due date:)

• Homework 3: (posted on, due date:)

• Homework 4: (posted on, due date:)

Reading Assignments (Textbook)

• Week 1: Section 1 （1.8 excluded, though you are welcomed to read it)

• Week 2: Sections 2-3

• Week 3: Sections 3-4

• Week 4: Sections 4-5

• Week 5: Sections 5-6

• Week 6: Review of Sections 1-6

• Week 7: Section 8.1

• Week 8: Section 8.2

• Week 9:

• Week 10: 

• Week 11:

• Week 12:

• Week 13:

• Week 14:

• Week 15:

• Week 16:

Topics for Oral Presentation

• Section 11.1 Estimation of Random Variables and Vectors（彭旭維、葉光豪）

• Section 11.2 Innovation Sequences and Kalman Filtering（吳紳文、黃楷勛）

• Section 11.3 Wiener Filters for Random Sequences

• Section 11.4 Expectation-Maximization Algorithm（胡誌宜、鄭濬緯）

• Section 11.5 Section Hidden Markov Models（許淯傑、徐子清）

• Section 11.6 Spectral Estimation（徐朝祐、許洹丞）

• Section 11.7 Simulated Annealing（呂彥霆、張哲維）

Reference Textbooks

1. Scott L. Miller and Donald G. Childers, Probability and Random Processes with Application to Signal Processing and Communications, 2nd, Elsevier Academic Press 2012. （東華書局代理，110學年用書）

2. Athanasios Papoulis and S. Unnikrishna Pillai, Probability, Random Variables and Stochastic Processes, 4th Ed., 2002 （歐亞代理）

"Fun" Readings

1. F. Mosteller, Fifty Challenging Problems in Probability with Solutions, New York: Dover Pub., 1965. [Link]

2. 老是覺得下一個會更好？科學教你：另一半的最佳挑選策略

3. Notes on the Euler-Maclaurin Summation Formula [Link]

4. T. M. Apostol. "An elementary view of Euler's summation formula," 1999. [Link]