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MATH 7880: Applied Stochastics (Spring '19)

The first two weeks will be a crash course in graduate probability: probability spaces, probability measures, integration, product spaces and product measures, conditional expectation, the law of large numbers, the central limit theorem, and martingales. We will not prove everything (this is rather the task of Math 6040). Instead, the emphasis is on bringing students who have not taken math 6040 up to speed, giving them enough working knowledge of these basic concepts, to allow us to use them in what follows. We will solidify the understanding of these concepts through a good amount of homework exercises that include some computations, some proofs, and some simulations.

After that, we will study random walk, Markov chains (both discrete and continuous time), Brownian motion, and diffusions and their connection to PDEs. As we go, we will also talk about some applications.

Email the instructor for access to the book.

If you need to brush up on some standard material in probability theory, Davar's book and Varadhan's notes are a good resource.

Homework 1 (due Tuesday February 5)

Homework 2 (due Thursday February 28)

Homework 3 (due Tuesday April 9)

Homework 4 (due Thursday May 2)