2009 Spring MATH 287-01
Bulletin Course Description Theoretic probability. Triangular arrays, weak laws of large numbers, variants of the central limit theorem, rates of convergence of limit theorems, local limit theorems, stable laws, infinitely divisible distributions, general state space Markov chains, ergodic theorems, large deviations, martingales, Brownian motion and Donsker's theorem. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title PROBABILITY Department MATH Course Number 2009 Spring 287 Section Number 01 Primary Instructor Huber,Mark Prerequisites Prerequisites: Mathematics 241 or Statistics 205 or equivalent. Course Homepage courses.duke.edu
Synopsis of course content
This course is meant to be a measure theoretical look at modern probability. The first few weeks will be spent reviewing measure theoretical concepts and theorems in a probability context. The next section will cover the central limit theorem and its extension to sequences of random variables that are not iid. Then random walks will be explored, which leads naturally into the second half of the course where the major types of stochastic processes will be examined, including martingales, Brownian Motion, and Markov chains. This includes chains on continuous state spaces.
This course differs from Math 216 (stochastic processes) in that measure theory will be used extensively throughout the course both in stating results and in developing the theory.
Textbooks
Probability: Theory and Examples, 3rd Edition by Rick Durrett
Assignments
There will be short homeworks due once a week.
Exams
There will be two midterms testing knowledge of major terms and theorems covered in the course.
Grade to be based on
Two midterms and the homework.
