STAT31120 (Spring, 2021)¶
Statistics 31120: Numerical Solution of Stochastic Differential Equations
Lecture: MW 4:10 PM-5:30 PM, over Zoom. Link can be found on Canvas Calendar .
Textbook: Milstein, Numerical Integration of Stochastic Differential Equations. Kloeden & Platen, Numerical Solution of Stochastic Differential Equations.
Course Syllabus syllabus.
Instructor: Zhongjian Wang (zhongjian at uchicago dot edu, urgent contact zhongjianwang25 at gmail dot com).
Office hours:
Zhongjian, Wed 3-4 PM, 7-8 PM. (Send me an email if you cannot enter the room).
Link to drop in can be found on Canvas Calendar .
Overview and prerequisites¶
This course aims to exhibit fundamental theories in numerical solution of stochastic different eqautions. It starts with a brief review of stochastic calculus and stochastic differential equations, then emphasizing the numerical methods needed to solve such equations. The stochastic Taylor expansion provides the basis for the discrete-time numerical methods for differential equations. The course presents many results on high-order methods for strong sample path approximations and for weak functional approximations. To help with developing an intuitive understanding of the underlying mathematics and hand-on numerical skills, examples and exercises on PC are included.
Knowledge of ODE and SDE is essential. STAT 39000 or STAT 39010 or STAT 38510 are strongly recommended.
Course Policies¶
Projects¶
There will be several projects. For each project, you need to send one PDF file to one of my email address (will announce during the first lecture and also on canvas). You may need some computing resources (like your laptop) and utilize any programming language to conduct numerical experiments. Due to the randomness, there is no reference solution to the project. It will be evaluated by completeness. You do not need to tex your reports out. Late submission is not accepted.
Grading¶
Exams: There will be one midterm exam and one final exam according to the following schedule.
Midterm: April 28.
Final Examination: Noon of June 4th 2021.
The use of notes, textbooks, or electronic devices are allowed during exams. No make-up exams will be offered without a letter from the dean or a doctor’s note. No make-ups are possible for the final exam.
The final course grade will be determined according to the maximum of the two following computations:
(50% Projects) + (50% Final)
(20% Projects) + (30% Midterm) + (50% Final)
Academic Integrity¶
I encourage you to work together on projects! The projects are intended to help you better understand the course material. Make sure understand what you write on the projects. When submitting your homework, you should cite any sources you used (in print, online, or human) other than the textbook and myself.
Students with disabilities¶
In order to receive disability-related academic accommodations, students must first be registered with Student Disability Services (SDS). More information on the SDS registration process is available here. Registered students must present an accommodation letter to the instructor before exam or other accommodations can be provided. Students who have, or think they may have, a disability are invited to contact SDS for a confidential discussion.
Materials¶
Lecture notes:
Getting Help¶
Peer Tutoring¶
UChicago offers peer tutoring via the Core Tutoring Program. See more information here.
Contact me¶
Please come during office hours, or email me for help if you are having difficulty with the material.
If you find anything on this website unable to access, feel free to raise an urgent issue to me.