This Ph.D. level course is intended to give students a broad sense of the different mathematical and computational tools and models available to analyze systems in which uncertainty is present. The key ideas underlying stochastic analysis will be presented in a mathematically careful way, and illustrated using various applications chosen from engineering, the physical sciences, and economics. This course is intended both to introduce students to the subject matter at an advanced level and to offer an entry point into the many other high-level stochastics courses that Stanford offers.
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|Time:||Tuesdays and Thursdays 11:00am-12:15pm
Knowledge of sample space, events, probability, conditional probability, independence, random variables, jointly distributed rvs, probability mass functions, probability density functions, expectations, the law of large numbers, central limit theorem.
Probability and Random Processes by Geoffrey R. Grimmett & David Stirzaker (Oxford)
Statistical Inference by George Casella and Roger L. Berger (Duxbury)
See Math 136 Lecture Notes by
Amir Dembo for a great treatment on probability theory
See also: Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues by Pierre Bremaud (Springer), Chapter 1, Sections 1 to 7
Familiarity with linear algebra, basic real variables and analysis, and differential equations is also useful.
There is no required textbook for this class. We will shortly post a concise listing of useful references.
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.
The midterm is Tuesday, May 3 in class. The midterm is closed
The final is Tuesday June 7 in Room 200-205 from 3:30-6:30pm.
The final is closed
book and closed note.
The course grade will be based on assignments (25%), the midterm (25%), and the final exam (50%).