Topics in Probability: Spring 2005
Math 7880-1
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Time & Place:	MWF 2:00-2:50 PM	JWB 308
		MWF 12:55-1:50 PM	LCB 222
		MW 4-5 PM, F 2-3 PM	JWB 208

Instructor:	Davar Khoshnevisan	JWB 102
					<my first name> aT math dOt utah dOt edu
					801-581-3896
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Course Outline:
We will concentrate on three themes:

 Ergodic and Subadditive Ergodic Theory; Markov Chains; 
  Stationary Processes
 Weak Convergence of Probability Measures in the Space 
  of Continuous Functions; Donsker's Theorem (weak
  convergence of random walks to Brownian motion)
 Elements of Large Deviations (estimation of exceedingly
  small probabilities)

It is possible that we may replace the third topic with "Elements
of Stochastic Differential Equations," but this will be decided
during the term.
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Text:
There isn't a fixed textbook for this course. However, I will
suggest a number of useful books, and make papers available,
if needed.
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Prerequisites:
Math 6040 and Math 6210; the first requirement will not be waived.
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Grading:
Every student is expected to turn in at least one of the assignments, 
and present one or two lectures on a related topic. The topic needs
to be approved in advance by the instructor.
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Announcements:

I will be out of the country the first two lectures. 
    Please attend the first lecture. There is no lecture on
    Wednesday 12th.
The lecture times will be changed to 12:55-1:50 PM. The room
    will be announced the first day of the lectures.
    Karim Khader will have the instructions.
(1/14) Note the new lecture time/place.
(1/21) Note the new lecture times/place.
(1/21) Some notes on the ergodic theorem. 
    More will be added later.
(2/12) Updated notes on the ergodic theorem.