Department of Computer Science, National Chiao-Tung University
IOC5127 Stochastic Processes
Time of Offering: Spring Term, 2017
Level: Graduate Students
Prerequisites: The recommended prerequisites are to have taken Elementary Probability Theory and Signals and Systems.
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
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.
Wen-Hsiao Peng (彭文孝), Ph.D.
Office: EC431 (工三館431)
LIAN-CHING, CHEN (陳蓮清) firstname.lastname@example.org
Room: EC 621 (工程三館)
The course meets on Wednesdays from 10:10am to 12:00pm (3CD) and Fridays from 16:30pm to 17:20pm (5H), in EC022.
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
· 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
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.
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).
50% Two mid-term exams (25% each)
30% Final Exam
Wednesdays/Fridays after classes in Engineering Building III Room 431.
Other time slots are also possible by appointments beforehand.