Dr. Gerard Brunick (PSTAT, UCSB)

Title: Weak uniqueness for a class of degenerate diffusions with continuous covariance

Abstract: Motivated by the problem of calibrating linear pricing rules to the market prices of options, we provide a new weak uniqueness result for degenerate diffusions. In particular, we consider path-dependent stochastic differential equations where the diffusion coefficient is a function of both the current location of the process and the running integral of the process, and we show that uniqueness holds for continuous, strictly positive-definite diffusion coefficients. These results combine tools from the theory of singular integrals on Lie groups with the localization machinery of Stroock and Varadhan.