**
MATH 285A: INTRODUCTION TO STOCHASTIC PROCESSES (SPRING 2001)
**

The last class meeting will be on Wednesday, June 13, 4.30-6.30 p.m. in
Peterson Hall 102.
** Professor: **
Professor R. J. Williams

** Time: ** MW 4.40-6 p.m.

** Place: ** Peterson Hall 104.

** Office Hours: ** M W 3-4 p.m.

**
DESCRIPTION: **
This one quarter course on stochastic processes is intended
to introduce beginning mathematics graduate students and graduate
students from other scientific and engineering disciplines to some
fundamental stochastic processes used in stochastic modeling. For the
mathematics students, this will provide valuable preparation and
motivation for the more advanced graduate probability sequence, Math
280ABC. For students from other disciplines, the course will provide
a theoretical basis for pursuing applied work involving
stochastic models.

** PREREQUISITES: ** Math 180A or Cognitive Science 245 or
equivalent probability course or consent of
instructor

** TENTATIVE COURSE TOPICS: **

Fundamental elements of stochastic processes.
Markov chains.
Hidden Markov models.
Martingales.
Brownian motion.
Gaussian processes.
** ASSESSMENT: ** Assessment for the course will be based on
homework assignments or a project to be chosen in consultation
with Professor Williams.

** TEXT: ** The following book will be used as a basic reference
and this will be complemented with other handouts (e.g., on
hidden Markov models) throughout the course.

G. F. Lawler, Introduction to Stochastic Processes, Chapman and Hall, New York, 1995.

The book by Karlin and Taylor, listed below, is also a good fundamental
reference, with many examples.
** REFERENCES: **

* General Stochastic Processes and Markov Processes: *

S. Karlin and H. M. Taylor, A First Course in Stochastic Processes,
Academic Press.
J. Norris, Markov Chains, Cambridge University Press,
1997.

* Hidden Markov Models: *

P. Clote and R. Backofen, Computational Molecular Biology, An Introduction, Wiley, 2000; Chapter 5.
L. Rabiner and B.-H. Juang, Fundamentals of Speech Recognition, Prentice Hall, 1993; Chapter 6.

Iain L. MacDonald and Walter Zucchini, Hidden Markov and other Models
for Discrete-valued Time Series, Chapman and Hall/CRC Press, 1997.

* Hidden Markov Models -- more advanced text: *
R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov Models: Estimation
and Control, Springer-Verlag, 1995.

* Brownian Motion: *

K. L. Chung, Green, Brown and Probability, World Scientific, 1995.

* Gaussian Processes: *

R. J. Adler, An Introduction to Continuity, Extrema and Related
Topics for General Gaussian Processes, IMS Lecture Notes--Monograph
Series, Vol. 12, 1990.
S. M. Berman,
Sojourns and Extremes of Stochastic Processes,
Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1992.

* Markov Chain Monte Carlo Simulation Methods: *
C. Robert
and G. Casella, Monte Carlo Statistical Methods, Springer, 1999.
C. Robert, Discretization and MCMC Convergence, Lecture Notes 135,
Springer, 1998.

* Markov Decision Processes *
M. L. Puterman, Markov Decision Processes, Wiley, 1994.

E. Altman, Constrained Markov Decision Processes, Chapman and Hall, CRC Press, 1999.

* Fitting Stochastic Models to Data: *

E. A. Thompson, Statistical Inference from Genetic Data on Pedigrees,
NSF-CBMS Regional Conference Series in Probability and Statistics, Vol. 6,
Institute of Mathematical Statistics, 2000.

B. J. T. Morgan, Applied Stochastic Modelling, Arnold Publishing, London, 2000.

* Selected Applications of Stochastic Modeling: *

P. Baldi and S. Brunak, Bioinformatics: The Machine
Learning Approach, MIT Press, Second Edition, 2001.
R. Durbin, S. Eddy, A. Krogh, and G. Mitchison, Biological Sequence
Analysis, Cambridge University Press, 1998.
M. S. Waterman, Introduction to Computational Biology, Chapman and Hall/CRC Press, 1995.
G. Winkler, Image Analysis, Random Fields, and Dynamic Monte Carlo Methods, Springer, 1995.
** SOFTWARE **

Hidden Markov Model Matlab Toolbox (GNU software)
** USEFUL INFORMATIONAL LINKS **

Web sources on hidden Markov models (under
construction)
Web sources on bioinformatics (under construction)
Obituary for N. Metropolis.
Brownian motion: a description of aspects of this process
and
some of its applications
(provided
by Y.K.Lee and Kelvin Hoon)

** Contact information: ** If you are interested in this course,
please send email to williams@math.ucsd.edu stating your background in
probability, your department
and any questions you might have.