2003 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 2003 Spring 287 Section Number 01 Primary Instructor Huber,Mark Lawrence Prerequisites Prerequisites: Mathematics 241 or Statistics 205 or equivalent. Course Homepage https://courses.duke.edu
Prerequisites
A course in measure theory, either Math 241, Stat 205, or an equivalent course.
Synopsis of course content
Measure theoretic treatment of Brownian motion and stochastic calculus followed by an introduction to other processes, in particular, stable processes (Levy processes) and fractional Brownian motion. We will begin the course with a brief review of the measure theory we will be using in the course, but this will be brief so students need to have had a course on measure theory such as Math 241 or Stat 205 at some point.
Textbooks
Karatzas and Shreve, Brownian Motion and Stochastic Calculus 2nd Edition
Assignments
Weekly assignments
Exams
There will be a midterm and exam. Both will mainly test familiarity with terminology and results we develop in the course.
Grade to be based on
Homework 50% Midterm 20% Final Exam 30%
