Math 635 Introduction to Brownian Motion and Stochastic Calculus

Spring 2014

Meetings: MWF 1:20-2:10, B139 Van Vleck
Instructor: Timo Seppäläinen
Office: 419 Van Vleck, Office Hours: after class MW or by appointment
Phone: 263-2812

This is the course homepage that also serves as the syllabus for the course. Here you will find updates on scheduling matters.

Math 635 is an introduction to Brownian motion and stochastic calculus without a measure theory prerequisite. Topics touched upon include sample path properties of Brownian motion, Itô stochastic integrals, Itô's formula, stochastic differential equations and their solutions. As an application we will discuss the Black-Scholes formula of mathematical finance.


Math 521 and Math 632 (that is, a good level of mathematical maturity and an introductory course on stochastic processes). If you need to review basics of probability theory, here is a brief handout.


Stochastic Calculus and Financial Applications by J. Michael Steele. Springer.

The heart of the material is in Chapters 6 and 8 of the book. Before we can define the Itô integral, we need to cover preliminaries such as conditional expectations, martingales and Brownian motion from Chapters 2-5.


Course grades will be based on a combination of homework and two exams.

Exam 1. In-class portion on Wednesday March 5, take-home portion due two days later.

Exam 2. Saturday May 3, 1-3 PM, VV B139, the usual classroom.


Spring 2014 Schedule

We will record our actual schedule here.

Instructions for Homework