Stochastic Systems (Spring 2015)
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.
Course Assistant: TBD
Time : M/W/F 11:00 AM - 12:15 PM (Note: Not all class periods will be used.)
Location : Thornton 110
Professor Glynn: TBA
Students taking this course are expected to have taken a basic course on stochastic processes at the level of MS&E 221 or STATS 217, and should have a familiarity with basic linear algebra. Students should also have an understanding of basic real analysis (i.e. rigorous understanding of limits, continuity, sequences and series, etc.).
Introduction to Stochastic Processes (Erhan Cinlar)
There will be four 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.
Late Policy: Late assignment submissions are NOT accepted (unless under extenuating circumstances with written documentation). All homeworks are due in class on the indicated due date. Hard-copies are preferred; electronic submissions (when submitted promptly) will be graded without comments.
There will be no midterm. The final will be 48-hour take-home.
The course grade will be based on assignments (50%) and final exam (50%).