Young Parabolic PDEs and the Martingale Problem for Young SDEs

Source abstract

Under mild regularity assumptions, we prove that the martingale problem associated with the hybrid Young--Lyons--Itô differential equation admits a unique solution in the natural class of solutions satisfying Krylov-type estimates, thereby establishing probabilistic weak well-posedness. Our proof relies on an 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.