CS285 Stochastic differential equations (Spring 2014)

From UCI Wiki hosted by EEE
Jump to: navigation, search

Contents

Course information

  • Title: An Introduction to Stochastic Differential Equations
  • 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

Textbook

  • Stochastic Differential Equations: An Introduction with Applications by Bernt ├śksendal


Homework

Exam

Preparing scribe notes