3:00 pm Friday, September 13, 2019
Junior Analysis: Gamma-martingales and BSDE by Joe Jackson in RLM 11.176
Martingales on manifolds, also known as gamma-martingales, form an important class of processes. One interesting question about gamma-martingales is the following: given a terminal condition (i.e. a manifold-valued random element) U, does there exist a unique martingale X which converges to U a.s. In 1995, Darling showed how to approach this problem using backward stochastic differential equations (BSDE). His techniques can be understood by analogy with geometric analysis - rather than using PDE to study geometry, Darling uses SDE to study stochastic geometry. In this talk, I will introduce stochastic differential equations and gamma-martingales, assuming only a basic knowledge of real-valued martingales and some definitions from Riemannian geometry. I will then present the main result of Darling's paper, and explain its significance in the field of stochastic analysis. Submitted by
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