• Title: 'An Introduction to Stochastic Differential Equations'
• Instructor: Xiaohui Xie
• Meeting information:
  • Regular lecture: TT 3:00-4:20
  • Meeting place: ICS 213

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

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

• [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]

• Stochastic Differential Equations: An Introduction with Applications by Bernt Øksendal

• [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.

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