SYLLABUS for : IEOR 6712. Stochastic Models II
Spring, 2014, Professor K. Sigman
This is a Ph.D. level course for first-year IEOR students in their second semester;
it is a continuation of IEOR 6711 "Stochastic Models I".
In general this is not for MS students: Only MS students with a strong mathematical background
and strong peformance in previous courses (such as IEOR 6711) should consider taking this
course (and they are welcome). Strong background means that the student feels comfortable with
some rigour and mathematical proofs.
This course will cover an introduction to
martingales in discrete and continuous time, Brownian motion,
an introduction to stationary point processes, and a brief introduction to stochastic calculus/differential equations in
the context of operations research. (Measure theory is not assumed/used.)
Detailed notes will be made available on the course website (students do not need to buy a book, but some excellent texts are suggested).
The level will
be that of Chapters 6 and 8 of S. Ross (1996) Stochastic Processes, Second Edition,
Wiley, New York; and Chapters 6 and 7 of Karlin and Taylor (1975) A First Course
in Stochastic Processes, Second Edition, Academic Press. Further references include
J. Michael Steele (2001) Stochastic Calculus and Financial
Applications, Springer-Verlag.
Bernt K. Oksendal (2003)Stochastic differential equations: An
introduction with applications,
Springer-Verlag.