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MATH 778:
Stochastic Processes (Spring
2007)
Instructor:
Soumik Pal
Meeting
Time & Room
The course objective is to cover a wide variety of topics in continuous
stochastic processes which depend on stochastic calculus and have gained
importance in probability or other areas in mathematics. First we will
create our toolbox: review of Ito calculus, martingales, and introduce
local times and some widely applicable results . Then we will use them
to analyse the following.
- Interplay between probability and differential
equations, particularly the heat and Feynman-Kac equations.
- Markov
processes.
- Some path properties of Brownian motion including occupation
time measures.
- Other fundamental processes: Brownian bridge, Ornstein-Uhlenbeck
and the Bessel processes.
On our way we will encounter some of the fascinating, deep theorems
of modern probability.
Course Outline
Last modified:October 31, 2006
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