Introduction to Stochastic Calculus (MATH 545, Spring 2019)

Meeting: Physics 259, Tue/Thu 3:05-4:20 p.m., replacement lectures: TBA

Instructor: Andrea Agazzi,

office hours: Physics 023, Thu 12:00-1:00 p.m. (from 1/14), or e-mail agazzi at math.duke.edu (please include MATH 545 in your email title).

Couse Description: This is an introductory, graduate-level course in stochastic calculus and stochastic differential equations, oriented towards topics that have applications in the natural sciences, engineering, economics and finance. A tentative schedule of topics is given below.

Prerequisites: Real analysis (MATH 431) and Probablity (MATH 230 or MATH 340). If you have not done well in these courses, you should consult the instructor before enrolling in this class. Some exposure to measure theory is a plus (via MATH 641 or equivalent), but it is not strictly required.

Sakai Website: All information on this course, syllabus, lecture notes, and homework assignments will also be progressively posted on the Sakai website. Log in with your NetID, and look for files under the "Resources" tab for our class.
You are encouraged to use the piazza website to ask questions about homework and class material; that way, the entire class can benefit from each question or comment.

Textbooks and references: The Principal Reference (required) of this course is

Here are some other useful texts, some of which will be available at the library: Some of these books are available at the library. Some unofficial lecture notes are available for download here. These noes will be periodically updated during the course and are not its main reference.

Grading: Judgement based on Final (30%) and Midterm (20%) exam marks and on consistent Homework efforts (50%).

Homework: HW1 (due JAN 24th), HW2 (due FEB 5th) HW3 (due FEB 19th) HW4 (due FEB 28th), HW5 (due MAR 21st), HW6 (due APR 4th).
Solutions: HW1_sol, HW2_sol, HW3_sol, HW4_sol, HW5_sol.

Please deliver your assignment during the class on the due date (late homework solutions will not be graded). Homework should be stapled, coherent and legible. Collaboration is allowed in solving the problems, but you are to provide your own independently written solution; copying answers is not allowed.

Reading: Reading assignments will be given with problem sets. You are expected to complete reading assignments before the corresponding class.

Tests: We will have one in-class midterm and one final exam. These tests will cover all class material, including ideas introduced in the homework problems, in the readings, and in class meetings. Taking the final is a necessary requirement for passing the class. No collaboration is allowed on exams. If you have to miss the in-class midterm, please arrange with the instructor at least a week ahead. In this case, you can only choose to take the exam earlier than the scheduled time.

Midterm: Thursday 3/7, 3:05-4:20 p.m., Room: Physics 259.

Final: TBA

Participation: Attendance to all class meetings is required.

Supplementary material: There is a good collection of problems posted on this website

Tentative Schedule of Topics (to be updated):