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• Instructor: David Anderson
• Office:  Van Vleck 617, phone: 608-263-4943
• email: anderson at math dot wisc dot edu
  
• Office hours: Tuesdays and Fridays: 1:00 - 2:30 PM.
• Lectures: Tuesdays and Thursdays, 9:30 - 10:45 AM, Room B139 in Van Vleck.

The syllabus can be found here.

Required Text:  Rick Durrett: Essentials of Stochastic Processes.  Available on Prof. Durrett's website.  Note that you do not need to purchase a book.  We will cover most of the topics in the text (plus a few extra). 

Course content:  The course consists of Chapters 1-4 from Durrett's book: discrete time Markov chains, Poisson processes, renewal processes, and continuous time Markov chains.  I also hope to cover at least a portion of chapter 5, martingales.  Further, I will have some extra topics such as simulation and applications in biology.  The course will begin with a review of basic probability (though this is *not* a substitute for having taken math 431 or equivalent).

Exams and Grades:  Course grades will be based on homework (25%), two midterm exams (25% each), and a final exam (25%).  No calculators/computers/phones in the exams. 

Exam dates:  First exam date: Night of Monday, October 15th.  Room B139 (same as class).  Time: 7:30pm - 9:30pm (show up at 7:15pm so you are not late!).
Second Exam Date: Night of Monday, December 3rd.  Room B139 (same as class).  Time: 7:30pm - 9:30pm (show up at 7:15pm so you are not late!).  -- This exam covers Branching processes, Chapter 2 (Poisson processes), Chapter 3 (Renewal Processes), and Chapter 4 (CTMCs).

Overview: 632 is a survey of some important classes of stochastic processes: Markov chains in both discrete and continuous time, point processes, and renewal processes. The material is treated at a level that does not require measure theory. Consequently technical prerequisites needed for this course are light: calculus, linear algebra, and an introduction to probability (at the level of Math 431) are sufficient. However, the material is sophisticated, so a degree of intellectual maturity and a willingness to work hard are required. For this reason some 500-level work in mathematics is recommended for background, preferably in analysis (521).

Good knowledge of undergraduate probability at the level of UW-Madison Math 431 (or an equivalent course) is required. This means familiarity with basic probability models, random variables and their probability mass functions and distributions, expectations, joint distributions, independence, conditional probabilities, the law of large numbers and the central limit theorem.  If you need a thorough review of basic probability, the textbook A First Course in Probability (on reserve in math library) by Sheldon Ross is recommended.

In class we go through theory, examples to illuminate the theory, and techniques for solving problems.   I will lecture using the blackboard on some days, and will present slide presentations on others (it will depend on the material).

A typical advanced math course follows a strict theorem-proof format. 632 is not of this type. Mathematical theory is discussed in a precise fashion but only some results can be rigorously proved in class. This is a consequence of time limitations and the desire to leave measure theory outside the scope of this course. Interested students can find the proofs in the textbook. For a thoroughly rigorous probability course students should sign up for the graduate probability sequence 831-832.

Check out the Probability Seminar for talks on topics that might interest you.