There is no required textbook for this course. The references
listed below contain material related to this course.
References:
C. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry,
and the Natural Sciences, Springer, 2004.
M. Grigoriu, Stochastic Calculus : Applications in Science and
Engineering, Birkhauser, 2002.
P. Kloeden and E. Platen, Numerical Solution of Stochastic
Differential Equations, Springer, 1999.
Prerequisites: Familiarity with probability,
a course in numerical methods,
and the ability to program a computer in a language such as
Fortran or C.
Examinations: There will be a midterm examination and a final
examination. The midterm examination will occur before the "drop'' deadline.
The final examination date, time, and location will be determined by the university.
Homework: Homework assignments/projects will be given frequently;
some will involve writing computer programs in a computer language such
as Fortran or C. Each assignment must be turned in at the beginning
of class. Late assignments are NOT accepted. Early assignments are
always welcomed and are appropriate for preplanned absences from class.
Your work must be shown in order to receive credit.
Grading: The midterm examination will represent 30% of your
grade. The final examination will also be worth 30% of your grade. The remaining
40% of your grade will be determined by your homework/projects.
Attendance: Attendance at and participation in all lectures
is expected. If you know in advance that you will be absent from class for
a legitimate reason, please tell me prior to your absence so that appropriate
arrangements (if any) can be made. Tardiness to class is very disruptive
of the classroom environment and should be avoided.
Honor Code: The NJIT Honor Code applies
to all activities associated with this course, including but not limited
to homeworks, projects, and examinations. As an example, when you submit
a homework assignment, you are certifying that your paper contains only your
work and is not copied from other people or sources.
Course Topics:
Introduction to stochastic processes, Brownian motion,
Weiner process, stochastic simulation
Stochastic integrals, stochastic calculus, Ito's formula,
Feynman-Kac theorem, Girsonov's theorem, stochastic Taylor series
Stochastic ordinary differential equations, analytical
and numerical solution techniques