STAT31120 (Winter, 2022)

Statistics 31120: Numerical Solution of Stochastic Differential Equations

Lecture: TTh 02:00 PM - 03:20 PM @ Jones Laboratory 226;

  • During remote-only instructional period, Zoom link will be posted on Canvas Calendar .

  • Door of Jones lab requires specifically coded access on UChicago Cards, please submit your application to Zellencia via Email.

Textbook: 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).

Grader: Hongli (Bob) Zhao (honglizhaobob at uchicago dot edu)

Office hours: Mon 2:00 PM - 5:00 PM @ Jones Laboratory 308 . You are not required to attend any office hours, as information that affects generally will discuss during the following lecture. Extra hours may be available given urgent necessity. I might be in my office (309) when there is no one present at 308.

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 Grader’s email address (honglizhaobob at uchicago dot edu ). 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.

Exams

There will be one midterm exam and one final exam according to the following schedule.

  • Midterm: Feb 10, covers up to (including) Lecture 8.

  • Final Examination: Mar 17, Noon

The exams are in form of 24-hours-take-home exams, however you have to do it by yourself. Hence 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.

Grading

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

You are strongly encouraged to work together on projects, but you must list all of your collaborators on the top of your homework. Using the ideas of another student without proper acknowledgement constitutes plagiarism, according to the University’s academic integrity policy.

All exams must be completed on your own - collaboration is prohibited. In general, you must carefully read and follow all of the exam rules. Any student found to have cheated in any way on any exam will receive a failing grade in the course and will be reported to the Dean.

Accommodations

The University of Chicago is committed to ensuring equitable access to our academic programs and services. Students with disabilities who have been approved for the use of academic accommodations by Student Disability Services (SDS) and need a reasonable accommodation(s) to participate fully in this course should follow the procedures established by SDS for using accommodations. Timely notifications are required in order to ensure that your accommodations can be implemented. Please meet with me to discuss your access needs in this class after you have completed the SDS procedures for requesting accommodations:

Materials

Lecture notes:

L1* L2 L3 L4* L5 L6 L7* L8 L9 L10* L11 L12 L13* L14 L15 L16

(*) projects assigned.

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 in accessing any course materials.