University of Utah
Department of Mathematics
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I will assume the student knows measure theory, for example from having taken a graduate probability course or a real analysis course. Topics that are assumed to be known are: measure spaces, measures, integration, product spaces and product measures. I will quickly run through these topics at the beginning of the course, but will not give any proofs. I will also run through conditional expectation, the law of large numbers, the central limit theorem, and martingales. Again, without any proofs. The goal of the first set of homework problems (HW0) will be to solidify the knowledge of these topics.
After that, we will study random walk, Markov chains (both discrete and continuous time), Poisson processes, Brownian motion, and diffusions and their connection to PDEs.
Homework 1 (due Sunday February 12)
Homework 2 (due Wednesday March 24)
Homework 3 (due Sunday April 9)
Homework 4 (due Sunday April 23)
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