Department of Computer Science, National Chiao-Tung University

IOC5127 Stochastic Processes

Ÿ             Time of Offering: Fall Term, 2009

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             Course Homepage


Ÿ             Lectures

­             The course meets on Mondays from 10:10am to 12:00pm and Wednesdays from 9:00am to 9:50am, in ED 305.

Ÿ             Course Outline

­             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

­             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

­             Random Sequences

·      Wide Sense Stationary Random Sequences

·      Markov Random Sequences

·      Convergence of Random Sequences

·      Law of Large Numbers

­             Random Processes

·      Poisson Process

·      Wiener Process (Brownian Process)

·      Markov Random Process & Birth-Death Markov Chains

·      Wide-Sense Stationary Processes and LSI Systems 

­             Advanced Topics in Random Processes

·      Ergodicity

·      Karhunen-Loeve Expansion

­             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 and Random Processes with Applications to Signal Processing, 3rd ed., Prentice Hall, 2001. (ISBN 0-13-020071-9)

­             (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. (ISBN 0-38-795578-X)

Ÿ             Grading Policy

­             25% Homeworks

­             30% Mid-term

­             45% Final Exam

Ÿ             Office Hours

­             Monday/Wednesday after class in Engineering Building III Room 431.

­             Other time slots are also possible by appointments beforehand.

Ÿ             Teaching Assistant

­             吳崇豪

­             TEL: ext59287

Ÿ             Miscellaneous

­         10/26~10/30 Attend MPEG Meeting in Xian, China

Ÿ             Connection with Other Courses