Description
Stroock--Varadhan martingale problem of Young stochastic differential equations
Under mild regularity assumptions, we prove that the martingale problem associated with the hybrid Young-Lyons-Itô differential equation admits a unique solution, thereby establishing probabilistic weak well-posedness. Our proof relies on analysis of the associated Kolmogorov equations, which are Young-type parabolic PDEs with irregular coefficients. The resulting theory for such Young-type parabolic PDEs is also of independent interest.
This talk is based on joint work with Fabio Bugini, Michele Coghi and Khoa Lê.