2010 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 theoerm. Additional topics have included one dimensional boundary behavior, stochastic averaging, stochastic numerical methods. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title STOCHASTIC CALCULUS Department MATH Course Number 2010 Spring 219 Section Number 01 Primary Instructor McKinley,Scott A Prerequisites Prerequisites: Undergraduate background in real analysis (Mathematics 139) and probability (Mathematics 135).
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 (We will discuss 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.
Exams
There will be one mid-term exam and a take home final.
Grade to be based on
Homework and exams.
Additional Information
There is no course web page. We will be using Blackboard for assignments and other class materials.
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