Department of Computer Science, National Chiao-Tung University

IOC5127 Stochastic Processes

Ÿ   Time of Offering: Spring Term, 2017

Ÿ   Level: Graduate Students

Ÿ   Prerequisites: The recommended prerequisites are to have taken Elementary Probability Theory and Signals and Systems.

Ÿ   Connections to other courses: This course is an extension of Elementary Probability Theory studied in your junior years and paves the way to studying more advanced
topics/subject matters that depend heavily on probabilistic frameworks, such as Bayesian Models for Machine Learning, Detection and Estimation, Information Theory,
Queuing Theory, Adaptive Signal Processing, Communications, Optimization, etc.

Ÿ   Course Instructor

­         Wen-Hsiao Peng (彭文孝), Ph.D.

­         E-mail:

­         Office: EC431 (工三館431)

­         Phone: Ext56625

­         Lab: Multimedia Architecture and Processing Laboratory (MAPL)

­         URL:

Ÿ   Teaching Assistant

­         LIAN-CHING, CHEN (陳蓮清)

­         Room: EC 621 (工程三館)

­         Phone: 56639

Ÿ   Course Homepage


Ÿ   Lectures

­         The course meets on Wednesdays from 10:10am to 12:00pm (3CD) and Fridays from 16:30pm to 17:20pm (5H), in EC022.

Ÿ   Course Outline

1.          Expectation and Introduction to Estimation

·      Moments & Moments Generating Functions

·      Chebyshev and Schwarz Inequality

·      Chernoff Bound

·      Characteristic Functions

·      Estimator for Mean and Variance of the Normal Law

2.          Random Vectors and Parameter Estimation

·      Multidimensional Gaussian Law

·      Characteristic Functions of Random Vectors

·      Parameter Estimation

·      Estimation of Vector Mean and Covariance Matrices

·      Maximum Likelihood Estimators

·      Linear Estimations of Vector Parameters

3.          Random Sequences

·      Wide Sense Stationary Random Sequences

·      Markov Random Sequences

·      Convergence of Random Sequences

·      Law of Large Numbers

4.          Random Processes

·      Poisson Process

·      Wiener Process (Brownian Process)

·      Markov Random Process & Birth-Death Markov Chains

·      Wide-Sense Stationary Processes and LSI Systems

5.          Advanced Topics in Random Processes

·      Ergodicity

·      Karhunen-Loeve Expansion

6.          Applications to Statistical Signal Processing

·      Conditional Mean, Orthogonality and Linear Estimation

·      Innovation Sequences and Kalman Filtering

·      Wiener Filters for Random Sequences

·      Hidden Markov Models

Ÿ   Lecture Notes

­         Lecture Notes (by Profs. David Lin and Sheng-Jyh Wang , NCTU EE)

­         Password is required for accessing the lecture notes and will be announced during the lectures.

Ÿ   Reference

­         Henry Stark and John W. Woods, Probability, Statistics, and Random Processes for Engineers, 4th ed., Prentice Hall, 2011 (Text).

­         Henry Stark and John W. Woods, Probability and Random Processes with Applications to Signal Processing, 3th ed., Prentice Hall, 2001 (for reference only).

­         (Chapter 7 and 8) K. L. Chung and F. AitSahlia, Elementary Probability Theory With Stochastic Processes and an Introduction to Mathmatical Finance, 4th ed., Springer-Verlag, 2003(for reference only).

Ÿ   Grading Policy

­         20% Homework

­         50% Two mid-term exams (25% each)

­         30% Final Exam

Ÿ   Office Hours

­         Wednesdays/Fridays after classes in Engineering Building III Room 431.

­         Other time slots are also possible by appointments beforehand.