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