# CS285 Stochastic differential equations (Spring 2014)

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## 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

- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 7
- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12
- Lecture 13
- Lecture 14
- Lecture 17
- Lecture 18
- Lecture 19

## Textbook

- Stochastic Differential Equations: An Introduction with Applications by Bernt Ã˜ksendal

## Homework

- Assignment #1 Due date: 04/17 (Thur) before class.
- Assignment #2 Due date: 05/01 (Thur) before class.
- Assignment #3 Due date: 05/15 (Thur) before class.
- Assignment #4 Due date: 05/29 (Thur) before class.

## Exam

- Final Exam Due date: 06/10 (Tues) before 5pm.