Current teachingFall 2016:
Honors I: Introduction to Stochastic Processes
Description: This course will be an introduction to stochastic processes. Topics to be discussed include Markov chains, Poisson process, Brownian motion, a little bit of Ito calculus, and some simulation methods like Markov Chain Monte Carlo. It will be a mixture of theory and applications, and will be as rigorous as it can without getting into measure-theoretic arguments.
The prerequisites are calculus, linear algebra, and probability theory. Although these are the only technical mathematical prerequisites, the course will assume a level of mathematical sophistication that goes beyond simply these raw courses; e.g. you should be comfortable with proofs, and with the higher-level mathematical arguments found in courses like analysis.
A little bit of programming will be required, but you do not have to have experience with this beforehand as we will cover the necessary elements in class. We will probably use Python for examples in class, but you could also use Matlab or R if you are more familiar with these.Textbook: Introduction to Stochastic Processes, by Robert Dobrow.
Available for purchase from the publisher or from amazon or the NYU bookstore.
- Applied Stochastic Analysis (Spring 2015). See here for lecture notes .
- Applied Stochastic Analysis (Spring 2014)
- notes on generating stationary Gaussian random fields
- Mathcamp 2008 Project Page
- Fall 2007 -- Written Exam Workshop
- Spring 2008 -- Calculus I