Class Meeting Information: MSB403 TuTh 12:30 - 1:45
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teplyaevmath.uconn.edu
http://www.math.uconn.edu/~teplyaev
office: MSB 426
office hours: TuTh 1:50pm--3:00pm (send me email before coming to confirm time)
Textbook: Diffusion Processes and Stochastic Calculus by Fabrice Baudoin -- (also available from amazon.com) -- (see also lecture notes)
Syllabus: The course will follow the textbook material, covering Chapters 1--6. It is expected that students will read all sections and solve exercises, and the difficulties encountered are to be discussed in class.
week | dates | chapter | sections | topics |
1st | 19,21 | 1 | 1--5 | stochastic processes: existence, continuity |
2nd | 26,28 | 1 | 6--7 | martingales |
3rd | 2,4 | 2 | 1--3 | Brownian motion |
4th | 9,11 | 2 | 4--5 | RWs, Donsker invariance principle |
5th | 16,18 | 3 | 1--2 | Markov |
6th | 23,25 | 3 | 3--4 | Feller-Dynkin, Levy |
7th | 1,3 | 4 | 1--3 | spectral theorem |
8th | 8,10 | 4 | 4--6 | Hille-Yosida |
9th | 22,24 | 4 | 7--9 | Dirichlet, Neumann |
10th | 29,31 | 5 | 1--3 | Ito |
11th | 5,7 | 5 | 4--7 | local martingales, Doeblin |
12th | 12,14 | 5 | 8--10 | time change, Burkholder-Davis-Gundy |
13th | 19,21 | 6 | 1--4 | SDEs, Feynman-Kac |
14th | 26,28 | 6 | 5--7 | Stratonovich, Malliavin |
Grading policy: Each week, a student is to choose 1 or 2 exercises to type complete solutions in latex, and submit pdf files or printouts (following instructor's feedback, some solutions may be revised and resubmitted).