EN257 Applied Stochastic Processes

Instructor: David B. Cooper
Office: Barus & Holley Room 318
Phone: 863-2601
E-mail: cooper@lems.brown.edu
Spring Semester, 2007
Graduate Level

Assignments:

• Assignment 1: click here to download
• Assignment 2: click here to download
• Assignment 3: click here to download
• Assignment 4: (due Wed, March 21) Problems: 6.10, 6.12, 6.13, 6.22 with additional problems passed out in class.
• Assignment 5:
  • Your text:  Problems  6.37;  6.40.
  • Larson and Shubert, vol 1. (the problems can be downloaded from here)
    • pp. 341, problem 9
    • pp. 342, problem 13
    • pp. 426, problem 7
    • pp. 427, problem 10, 11
• Last Assignment: you can download the problems 4, 6, 7, Section 2.3 of Larson & Shubert book here. [download].

Texts:

• Probability and Random Processes with Applications to Signal Processing, 3rd edition, by J. Woods and H. Stark Prentice Hall, 2002, ISBN 0130200719.
• Statistical Signal Processing, by L. Scharf, Addisen-Wesley, 1990, ISBN 0201190389.

Pertinent Books:

• Probabilistic Models in Engineering Sciences vols. 1 and 2, by H. Larson and B. Shubert.
  Vol. 1 is John Wiley, 1979, and is out of print.
  Vol. 2 is Krieger Press reissue of John Wiley 1979.
  I like these a lot!
• Probability and Random Processes, by Geoffrey Grimmett and David Stirzaker, 3rd edition.
  Oxford University press, 2001, ISBN-10: 0-19-857222-0, ISBN-13: 978-0-19-857222-0
  Good readable presentation of the mathematical approach.
• Probability, Random Variables and Stochastic Processes, by A. Papoulis and S.U. Pillai,
  4th or latest edition. McGraw Hill, 2002.
  Poorly organized and so so presentation, but has a lot of useful material for engineers.
• Random Processes, A Mathematical Approach for Engineers, by R. Gray and L. Davisson, Prentice Hall, 1986

Among topics to be covered:

• Brief review of probability spaces and random variables as functions on probability spaces, probability measures and distributions, joint distributions, functions of random variables.
• Quadratic forms and Multivariable Gaussian distributions. Characteristic functions.
• Estimation of random vectors as projections in linear spaces.
• Conditioning and its relation to estimation.
• Wiener Processes.
• Various types of convergences of sequences of random variables.
• Markov and Gauss-Markov processes.
• A touch of Martingales.
• Representations of stochastic processes in the time domain, the Wold Decomposition, and in the frequency domain, the Spectral Representation.
• The Kalman Filter.
• Tracking of objects in images.
• Markov Random Fields and some uses.

Prerequisites:

Roughly half the material will come from the text, and the remainder from other textbooks and papers which will be listed on the course web page.

If you are taking the course for credit, please e-mail your name, e-mail address, and department and year to davidbcooper@cox.net and to his secretary Richard_Minogue@brown.edu