MATH 5161: Probability Theory and Stochastic Processes II -- Spring 2016

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).