2006 Spring MATH 219-01
Bulletin Course Description Introduction to the theory of stochastic differential equations oriented towards topics useful in applications. Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations. Functionals of diffusions and their connection with partial differential equations. Ito's formula, Girsanov's theorem, Feynman-Kac formula, Martingale representation theorm. Additional topics have included one dimensional boundary behavior, stochastic averaging, stochastic numerical methods.
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title STOCHASTIC CALCULUS Department MATH Course Number 2006 Spring 219 Section Number 01 Primary Instructor Mattingly,Jonathan Permission required? N Course Homepage www.math.duke.edu/~jonm/Courses/Math219
Prerequisites
Basic real analysis and probability.
This course is intended to be accessible to a wide range of students including those in the sciences,, finance, statistics, engineering, as well as mathematics. If you have a question, contact the instructor.
Synopsis of course content
An introduction to the theory of stochastic differential equations
with an eye towards those topics useful in applications.
Brownian motion, stochastic integrals, and diffusions as solutions of
stochastic differential equations. Functionals of diffusions and their
connection with partial differential equations. Ito's formula,
Girsanov's theorem, Feynman-Kac formula, Martingale representation
theorem. Additional topics have included one dimensional boundary
behavior, stochastic averaging, stochastic numerical methods.
Textbooks
There are two suggested books (More about which to buy if any at the start of the class):
Stochastic Calculus: A Practical Introduction by Rick Durrett
Stochastic Differential Equations: An Introduction with Applications by Bernt Oksendal
Assignments
There will be regular assignments during the semester and possibly presentations at the end.
Grade to be based on
Homework and presentations
