Class Times, Days, and Place: 10:00-10:50 MWF, Deady Hall
209
Instructor: Hao Wang
Textbook: Instructor's Lecture Notes
Reference Book: (1) Stochastic Calculus by Richard Durrett ;
(2) Continuous Martingales and Brownian Motion by D. Revuz
and M. Yor
(3) Stochastic Differential Equations and Diffusions by N. Ikeda and S.
Watanabe
(4) Brownian Motion and Stochastic Calculus by I. Karatzas, S.E.
Shreve
Office: 11A Deady Hall
Office Hours: M:10:50-11:30pm and W:10:50-11:30pm (Otherwise,
you need to make an appointment with me by e-mail.)
Web URL:
http://darkwing.uoregon.edu/~haowang/teaching/672_WIN2006/672.html
Tentative Coverage: This course is intended to cover
following
contents:
(1) Conditional expectation and Markov property
(2) Transition functions and strong Markov property
(3) Semigroup and infinitesimal operators and Hille-Yosida Theorem
(4) Diffusion processes
(5) Backward and forward equations
(6) Examples
(7) Purely-discontinuous Markov processes
(8) Branching processes
(9) 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.