Math 672
(25900)
Class Times, Days, and Place: 14:00-14:50 MWF, DEA 209
Instructor: Hao Wang
Textbook: Instructor's Lecture Notes
Reference Book: (1) Probability and Measure by P. Billingsley
(2) Stochastic Calculus by Richard Durrett ;
(3) Continuous Martingales and Brownian Motion by D. Revuz and M. Yor
(4) Stochastic Differential Equations and Diffusions by N. Ikeda and S.
Watanabe
(5) Brownian Motion and Stochastic Calculus by I. Karatzas, S.E. Shreve
Office: 11A DEA
Office Hours: W:12:50-1:50pm and F:10:00-11:00am (Otherwise, you need to
make an appointment with me by e-mail.)
Web URL: http://uoregon.edu/~haowang/teaching/672_WIN2010/672.html
<>Tentative Coverage: This course is
intended to cover following contents:
(1) Measure Theory
(2) Advanced Probability
(3) Conditional expectation and Markov property
(4) Transition functions and strong Markov property
(5) Semigroup and infinitesimal operators and Hille-Yosida Theorem
(6) Diffusion processes
(7) Backward and forward equations
(8) Examples
(9) Purely-discontinuous Markov processes
(10) Branching processes
(11) Stationary processes
Homework and presentations: Since this is an advanced
probability course, we will arrange that the activities of learning and doing
research
are combined together. Some questions and problems with different degrees
of challenging are assigned as homework questions or research questions.
In order to well digest the contents of this course and improve the research
ability, during the term, two or three times of homework presentations or
question discussions will be organized. Homework is due weekly before
Monday's lecture. Homeworks and presentations will partially contribute to your
final grade.