==== Math 227C / CS 285: An Introduction to Stochastic Differential Equations ====

== Course information ==
  * Instructor:  Xiaohui Xie
  * Meeting information: 
    * Regular lecture: TT 3:00-4:20
    * Meeting place: ICS 213

== Prerequisites ==
  * multivariate calculus, linear algebra, elementary differential equations (at the level of Math 3D at UCI), and (helpful to know) some elementary probability

== Course Description ==
Tentative topics:
  *  Markov Chains and Linear Difference Equations
  *  Continuous Time Markov Processes
  *  Poisson Counters and Differential Equations
  *  Wiener Processes and Differential Equations
  *  Ito's calculus and Ito Formula
  *  Diffusion, Fokker-Planck Equations
  *  Probability space, Foundation of stochastic processes
  *  Conditional Expectation, Martingales
  *  Markov Properties, Feymann-Kac Theorem, Kolmogorov backward equation
  *  Application to stochastic control
  *  Application to filtering problems
  *  Application to population genetics

== Lecture notes ==
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/CourseScribeNotes.pdf Combined scribe notes]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture1.pdf Lecture 1]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture2.pdf Lecture 2]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture3.pdf Lecture 3]
  * [http://www.ics.uci.edu/~xhx/courses/math227c/lecture4.pdf Lecture 4]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture7.pdf Lecture 7]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture9.pdf Lecture 9]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture10.pdf Lecture 10]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture11.pdf Lecture 11]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture12.pdf Lecture 12]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture13.pdf Lecture 13]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture14.pdf Lecture 14]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture17.pdf Lecture 17]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture18.pdf Lecture 18]
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/lecture19.pdf Lecture 19]

== Textbook ==
  * Stochastic Differential Equations: An Introduction with Applications by Bernt Øksendal


== Homework ==
  *  [https://eee.uci.edu/14s/35340/home/ps1.pdf Assignment #1]  Due date: 04/17 (Thur) before class.
  *  [https://eee.uci.edu/14s/35340/home/ps2.pdf Assignment #2]  Due date: 05/01 (Thur) before class.
  *  [http://www.ics.uci.edu/~xhx/courses/math227c/ps3.pdf Assignment #3]  Due date: 05/15 (Thur) before class.
  *  [https://eee.uci.edu/14s/35340/home/ps4.pdf Assignment #4]  Due date: 05/29 (Thur) before class.

== Exam ==
  * [https://eee.uci.edu/14s/35340/home/final14.pdf Final Exam] Due date: 06/10 (Tues) before 5pm.