Stochastic Differential Equations

MATH8008, Spring semester, 2020

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 2925CGD 530.
Office Hours: MWF morning walk-in, other time by appointment.
Class meeting: MWF 10:10am - 11:05am, 2925CGD 608.

Textbook (recommended)

• Stochastic Differential Equations. An introduction with applications. Øksendal, Bernt. Sixth edition. Universitext. Springer-Verlag, Berlin, 2003.
• Stochastic Calculus and Financial Applications, Michael Steele. Applications of Mathematics (New York), 45. Springer-Verlag, New York, 2001.
• An Introduction to Stochastic Differential Equations, Lawrence Evans. American Mathematical Society, Providence, RI, 2013.

Course description

This course provides an introduction to stochastic calculus and stochastic differential equations. The lectures will roughly follow Chapters 2-5 and 7, and a few others if time permits, of Oksendal's book.

The homework will then focus on simulation methods for stochastic processes and SDEs, demonstrated by their applications to a few selected examples in applied areas.

Grades

• Grading: there will be 2-3 homework problem sets and a small project based on research papers.

Tentative Schedule

• Week 1 (Jan 13): Chapter 2, Brownian motion.
• Week 2 (Jan 20): No class on MLK, Monday (Jan 20).
• Week 3 (Jan 27):
• Week 4 (Feb 3): Chapter 3, Ito integrals.
• Week 5 (Feb 19):
• Week 6 (Feb 17):
• Week 7 (Feb 24):
• Week 8 (Mar 2):
• Week 9 (Mar 9):
• Week 10 (Mar 16): Spring Break.
• Week 11 (Mar 23):
• Week 12 (Mar 30):
• Week 13 (Apr 6):
• Week 14 (Apr 13):
• Week 15 (Apr 20):

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