MATH 275C: Spring 2013

MATH 275C: Spring 2013

Graduate Probability

lecturer: Marek Biskup, MS 6180
time and place: MWF 9:00-9:50 in MS 6227
office hours: TBA

General information: Check out the course announcement for general announcement.

Synopsis: This is the 3rd quarter of the 3-quarter UCLA graduate probability sequence. The following plan describes our main points of interest:

Ergodic theory
Stochastic processes with independent increments
Markov processes on general state spaces
Stochastic calculus

The prerequisites include good command of measure-based setup for probaility theory including familiarity with probabilist's (as opposed to analyst's) notations for various objects.

Homework & Final exam: There will be about 5 homework assignments during the quarter. The course will be finished with a take-home final exam (to be submitted in PDF online).

Literature & resources:

A principal textbook for this part of the course is

T.M. Liggett, Continuous-time Markov processes, AMS

Further material will be drawn from the following textbooks:

R. Durrett, Probability: Theory and Examples, Cambridge Univ. Press.
K.E. Petersen, Ergodic Theory, Cambridge Univ. Press.
I. Karatzas and S. Shreve, Brownian motion and stochastic calculus, Springer.