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 |
---|---|---|

1 | 1.1, 1.2, 1.3 | 9/17 |

2 | 2.1, 2.2 | 9/24 |

3 | 2.3, 2.4, 3.1, 3.2, 3.3 | 10/8 |

4 | 2.5, 2.6, 3.4, 3.5 | 10/29 |

5 | 6.1, 7.5, 12.1 | 11/7 |

**Instructor:** Richard Sowers

**Office:** 301 Transportation Building (IESE) and 347 Illini Hall (Math)

**Phone:** (217) 333-6246

**email:** r-sowers@illinois.edu (note; this email may be forwarded to an off-campus email address)

**Home page:** https://math.uiuc.edu/~r-sowers

**Class meets:** MWF 2-3:30 in 141 Altgeld Hall

**Office Hours:** M 8-10 AM at 301 TB and by appointment

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 |