Syllabus for Math 562, Section E1

Fall 2008, CRN 33567

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).

Provisional Schedule

Grading: Grades will be determined on the basis of homework (30%), a midterm (30%) and a final (40%).
Text: Øksendal, Stochastic Differential Equations, Springer-Verlag, 6th ed., 2003
Additional Reference: Karatzas and Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag

Instructor: Richard Sowers
Office: 347 Illini Hall
Phone: (217) 333-6246
email: r-sowers@illinois.edu
Home page: https://math.uiuc.edu/~r-sowers
Class meets: MWF 1-2 in 447 Altgeld Hall
Office Hours: MW 11:30-1

killed Brownian Motion