Department of Computer Science, National Chiao-Tung University

IOC5127(5196) Stochastic Processes

Ÿ   Time of Offering: Spring Term, 2014

Ÿ   Level: Graduate Students

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

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

­         Syuan-Yu Sie(謝璿羽)

­         Room: ES 704 (電子資訊大樓)

­         Phone: 59267

Ÿ   Course Homepage


Ÿ   Lectures

­         The course meets on Wednesdays from 10:10am to 12:00am (3CD) and Fridays from 15:30pm to 16:20pm (5G), in ED102.

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 Prof. Sheng-Jyh Wang 王聖智, 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. (ISBN-10: 0132311232)

­         (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, 2003. (ISBN-10: 1441930620)

Ÿ   Grading Policy

­         40% Homeworks

­         30% Mid-term

­         30% Final Exam

Ÿ   Office Hours

­         Wednesdays/Fridays after classes in EC431.

­         Other time slots are also possible by appointments beforehand.

Ÿ   Miscellaneous

­         Mar. 26th – Apr. 4th, MPEG meeting in Spain

­         Jun. 1st – Jun. 4th, IEEE ISCAS in Australia

(Missed lectures will be made up with times and places announced in due course)

Ÿ   Connection with Other Courses