ECE6558 Course Syllabus

ECE6558

Stochastic Systems (3-0-3)

Prerequisites

CEE/ISYE/MATH 3770

Corequisites

None

Catalog Description

Advanced techniques in stochastic analysis with emphasis on stochastic dynamics, nonlinear filtering and detection, stochastic control and stochastic optimization and simulation methods.

Textbook(s)

No Textbook Specified.

Topical Outline

Introduction
     Stochastic dynamic problems in control, communication and signal
         processing
     Review basic probability

Probability and stochastic analysis
     Random walks and Brownian motion
     Stochastic integrals and martingales
     Stochastic differential equations and Ito calculus

Stochastic Systems
     Stochastic stability
     Evolution equation: Kolmogorov and Fokker-Planck

Optimal Estimation
     Static estimation: linear and nonlinear
     Explicit solutions and approximations

Stochastic Control
     Optimal stochastic control: Full information case
     Optimal stochastic control: Partial information case
     Separation principle and LQG-design
     Dynamic programming, value functions, verification theorem

Applications in Communication and Signal Processing
     Cycle slip in phase locked loop
     Propagation in random media
     Simulated annealing and Monte Carlo simulation