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Graduate Seminar

Yangxi Ou
Carnegie Mellon University
Title: Gambling houses and reductions

Abstract: Modern potential theory lies at the intersection of analysis and probability and extends both subjects to an amazing generality. After familiarizing ourselves with kernels, excessive functions and sweeping, we will look at the object gambling house, which captures the mathematical nature of a literal gambling house, in the language of potential theory. Reduction is then introduced to analyze a gambler's value function, an approach different from the more popular dynamic programming. Time permitting, we will show a theorem of Sudderth, implying that stationary Markov strategies could be almost optimal playing in a gambling house. We follow the classic text Probabilities and Potential, Volume C.

Date: Tuesday, November 7, 2017
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Yangxi Ou
Note: Video on YouTube: https://youtu.be/UBPhkDvbn6w