Syllabus for Math 562, Section F1

Fall 2011, CRN 33567 and 33568

Theory of Probability, II

Gaussian Distribution

Roughly, this is a course about stochastic differential equations and the associated ideas of Ito calculus. We hope to understand both of these subjects and understand some of their structure. By structure, we mean some different perspectives and applications which reveal different perspectives on the material. Our goal will be to present this knowledge in a way which will be accessible to engineers who possess a certain level of mathematical maturity and at the same time to be precise enough that the mathematics student should have little trouble filling in the details. While Math 561 is not a prerequisite, you should be willing to dig through the notes for that class (which are online) to fill in as much detail as you need. Similarly, while you are not required per se to know measure theory, you should be able to become comfortable with the usage of measure theory (I will give a brief summary of the relevant portions of measure theory as needed).

Grading: Grades will be determined on the basis of homework (30%), a midterm (30%) and a final (40%). I will attempt to announce things on my Twitter Feed.
Primary Text: My Notes
Additional Texts
Øksendal, Stochastic Differential Equations, Springer-Verlag, 6th ed., 2003
Karatzas and Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag


Assignment number Problems Due Date
11.1, 1.2, 1.3 9/17
22.1, 2.2 9/24
32.3, 2.4, 3.1, 3.2, 3.3 10/8
42.5, 2.6, 3.4, 3.5 10/29
56.1, 7.5, 12.1 11/7


Instructor: Richard Sowers
Office: 301 Transportation Building (IESE) and 347 Illini Hall (Math)
Phone: (217) 333-6246
email: (note; this email may be forwarded to an off-campus email address)
Home page:
Class meets: MWF 2-3:30 in 141 Altgeld Hall
Office Hours: M 8-10 AM at 301 TB and by appointment

killed Brownian Motion

Richard Sowers
University of Illinois at Urbana-Champaign
Department of Industrial and Enterprise Engineering
College of Engineering
117 Transportation Bldg, MC-238
104 S. Mathews Ave., Urbana, IL 61801
Department Main Office Telephone: (217) 333-2731 Fax (217) 244-5705

Department of Mathematics
College of Liberal Arts and Sciences
273 Altgeld Hall, MC-382
1409 W. Green Street, Urbana, IL 61801 USA
Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576