(STA 3047F, Fall 2001)
Time and place:
Wednesdays, 6:10 to 9:00 p.m.
Sidney Smith Hall room 1080.
First class September 12; last class December 5.
Professor Jeffrey S. Rosenthal,
Department of Statistics, University of Toronto
Office hours TBA.
Sidney Smith Hall, room 6024; phone (416) 978-4594; contact me;
We will investigate stochastic processes in discrete and continuous time,
with emphasis on their convergence properties in various topologies
(including total variation distance and weak convergence). Examples of
processes will include Markov chain Monte Carlo algorithms and point
processes, with additional examples selected based on student interests.
STA 2111H (Graduate Probability I), or equivalent knowledge of
probability theory, measure theory, and real analysis.
(The course is designed primarily for Statistics PhD students.)
The following references may be helpful at times:
Homework 70%, Class Participation 30%.
Class Participation involves attending class regularly, answering
questions in class (such as helping to summarise the previous class),
and posing questions in class.
For basics of total variation distance convergence: J.S. Rosenthal
(1995), Convergence rates of Markov chains, SIAM Review 37, 387-405
(available from the instructor's web page).
For weak convergence and point processes: B. Fristedt and L. Gray (1997),
A modern approach to probability theory, Birkhauser, Boston (to be held
on reserve in the Math/Stat Library).
For MCMC and spatial point processes: J. Møller (1999), Markov chain
Monte Carlo and spatial point processes. In Stochastic Geometry:
Likelihood and Computations, Eds. O.E. Barndorff-Nielsen, W.S. Kendall
and M.N.M. van Lieshout, Monographs on Statistics and Applied Probability,
Boca Raton, Chapman and Hall/CRC, 141-172. (I can provide photocopies
For the Erdos-Turan Theorem: L. Kuipers and H. Niederreiter (1974),
Uniform distribution of sequences, John Wiley & Sons. Also H.
Niederreiter and W. Philipp (1973), Duke Math. J. 40, 633-649.
This document is available at http://probability.ca/jeff/courses/sta3047-01a.html.