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EE 531
Stochastic Processes
Course Description:
The course goal is to present random processes at the level of Stochastic Processes by Ross. Courses with similar titles appear in undergraduate curriculum. This course is expected to solidify the basic probability foundation given at the undergraduate level and study the stochastic processes with their applications. At the end of course, students should have the necessary background for statistical DSP, communications, queuing theory studies.
Course Outline:
- Introduction
to Probability
- Finite sets,
events on real line, events on function spaces etc.
- Random variables
- Moments,
characteristic functions, conditional moments
- Sequence
of random variables
- Correlation
matrix, covariance matrix
- Auto-correlation
sequence, power spectrum density
- Convergence
of random sequences
- Random
Processes
- Stationarity
- Wide sense
stationarity
- Ergodicity
- Processing
of random processes with linear time invariant systems
- Important
Random Processes
- Poisson
process
- Markov chains
(discrete time)
- Brownian
Motion, level-crossing problems, continuous time Markov chains,
martingales (as much as time permits)
Textbooks:
1.
Sheldon
Ross, Introduction to probability models
(8th Edition), Academic Press, 2003 (for
the first half of the coursem, other topics are lightly covered)
2.
Sheldon
Ross, Stochastic Processes (2nd Edition), John Wiley and Sons, 1996. (for
the second half of the course, requires some probability background)
3.
A.
Papoulis, Probability,
Random Processes and Stochastic Processes, (3rd edition or later), Mc-Graw
Hill, 1991. (not required, but highly recommended)
Evaluation: Homework assignments (some of them has
Matlab problems), two midterms and a final. Announced quizes are also planned.
Instructor: Çağatay Candan, C-105, 210-2355,
ccandan.at.metu