Math 635 - An Introduction to Brownian Motion and Stochastic Calculus

• Prerequisites: Math 521 and 632.
• Frequency: Irregular.
• Student Body: advanced undergraduate and graduate students
• Credits: 3. (N-A)
• Recent Texts: Steele, J. Michael. Stochastic calculus and financial applications. Applications of Mathematics (New York), 45. Springer-Verlag, New York, 2001.
• Course Coordinator: Jim Kuelbs.
• Background and Goals: This course is an introduction to Brownian motion, stochastic calculus, and some applications. The course does not require knowledge of measure theory. It is advisable to have some prior familiarity with elementary probability and stochastic processes.
• Alternatives: N/A
• Subsequent Courses: n/a

Content coverage:

• Brownian motion
• Ito stochastic integrals
• Ito's formula
• Stochastic differential equations and properties of their solutions
• Applications including finance