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ECE 64300 - Stochastic Processes in Information Systems

Credits: 3

Areas of Specialization(s):

Communications, Networking, Signal & Image Processing

Professional Attributes

Normally Offered: Spring - even years

Catalog Description:
Many different communication and information systems will be examined, with the emphasis on determining the fundamental questions each one poses. For instance, an examination of computer networks and computer systems will be shown to lead to questions about conditions which guarantee stable operation, while an examination of optical communication systems will lead to questions about communications in the presence of impulsive noise. Other examples that will be used include estimation in dynamic environments, speech modeling, signal detection, and the modeling of neural processes. The stochastic processes that will be developed for the modeling and analysis of these systems include: Markov Chains and Processes; Point Processes: Brownian Motion; and Martingales.

Required Text(s):
  1. Stochastic Processes, S. Ross, Wiley & Sons, N.Y, ISBN No. 0-471-12062-6.

Recommended Text(s): None.

Lecture Outline:

Lectures Topic
5.0 1. Fundamentals A. Probability spaces, measures, and random variables (1.0) B. Convergence concepts for events and random variables (2.0) C. Conditional Expectations and probabilities (1.0) D. Stochastic processes - definition, continuity concepts (1.0)
11.0 2. Point Processes A. Context: optical communications and impulsive noise B. The poisson process (4.0) C. Compound poisson processes and stochastic calculus (3.0) D. Doubly stochastic poisson processes (4.0)
10.0 3. Markov Chains and Processes A. Context: Stability questions in networks and speech modeling. B. Markov Chains 1. Definition and types of states (2.0) 2. Recurrence concepts (3.0) 3. Limiting behavior (3.0) 4. Random walks and networks B. Markov Processes 1. Definition and types (1.0) 2. Continuous time chains
5.0 4. Gaussian processes A. Context: recursive estimation and limits B. Weiner and Orstein-Ulenbeck processes (3.0) C. Stochastic Calculus (2.0)
8.0 5. Martingales A. Context: recursive estimation and limits B. Histories and stopping times (1.0) C. Definition and properties of martingales (2.0) D. Predictability and the Doob-Meyer decomposition (2.0) E. Recursive estimation and limit theorems (3.0)
2.0 6. Exams