MS&E 321 |
Stochastic Systems |
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General Information
Course
Description
This course addresses fundamental topics in the
modern theory of stochastic processes, with emphasis on a broad spectrum of
applications in engineering, economics, finance, and the sciences. The course
carefully treats Markov chains in discrete and continuous time,
Perron-Frobenius theory, Markov processes in general state space (including
Harris chains), Lyapunov functions and supermartingale arguments for establishing
stability, theory of regenerative processes and related coupling ideas, rare
event analysis via large deviations, renewal theory, martingales, Brownian
motion, and associated diffusion approximations. At the conclusion of this
course, students will have a working knowledge of the mathematical tools and
models that represent the cutting edge in the theory and application of
stochastic processes to complex systems. The ideas will be illustrated by
appealing to examples chosen from queueing theory, inventory theory, and
finance.
Instructor:
Professor Peter Glynn
Office: Huang Engineering Center, Room 326
Email: [email protected]
Course Assistant:
Jing Ma
Office: Huang Engineering Center, Room 314S
Email:
[email protected]
Lectures
Time : M/W/F
11:00 AM - 12:15 PM (Note: Not all class periods will be used.)
Location : 380-381T
Office Hours
Professor Glynn : 2 PM to 3 PM Thursdays at Huang 326
Jing Ma : 10:00 AM to 11:00 AM Thursdays and 1:30 PM to 2:30 PM Fridays at Huang B007
Prerequisites
Students taking this
course are expected to have taken a basic course on stochastic processes at the
level of MS&E 221 or STAT 217, and should have a familiarity with basic
linear algebra. Ideally, students should also have an understanding of basic
real variables (i.e. rigorous understanding of limits, convergence, etc.).
Textbook
Adventures in Stochastic Processes, by S.I. Resnick. Birkhauser, Boston (1992). (Note this is available as a Kindle reader, as well as in hard copy form; see Amazon)
Homework
There will be assignments due roughly every two weeks. Collaboration among students is encouraged. You should feel free to discuss problems with your fellow students (please document on each assignment with whom you worked). However, you must write your own solutions, and copying homework from another student (past or present) is forbidden. The Stanford Honor Code will apply to all assignments, both in and out of class.
Exams
There will be no midterm. The final
will be a 48 hours take-home.
Presentation:
To encourage you to think about how the course concepts apply to problems of direct interest to you, you are asked to select one or two papers from the current literature that build upon the tools discussed in this course. You will be asked to make a short presentation to the class at the end of the quarter, to provide your slides, and to generate a short written report on your selected topic. (A couple of pages would be fine. Please discuss (at a high level) the main results, and possible further research directions.) Please send your thoughts regarding potential papers to Professor Glynn and Jing Ma by February 6th.
Grading
The course grade will be based on assignments (40%), presentation/write-up (20%) and the final exam (40%).
| Management Science & Engineering
Dept | Stanford University |