MATH 285A: INTRODUCTION TO STOCHASTIC PROCESSES (SPRING 2001)
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Professor: Professor R. J. Williams
Time: The time is to be arranged, but the class is likely to meet twice a week for 80 minutes each time.
Place: TBA
Office Hours: TBA

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.

    REFERENCES:
    General Stochastic Processes:

  • S. Karlin and H. M. Taylor, A First Course in Stochastic Processes, Academic Press.
  • G. F. Lawler, Introduction to Stochastic Processes, Chapman and Hall, New York, 1995.
    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.
    Hidden Markov Models -- more advanced text:
  • R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov Models: Estimation and Control, Springer-Verlag, 1995.

    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.