| Abstract: |
| Under mild regularity assumptions, we prove that the martingale problem associated with the hybrid Young-Lyons-It\^o differential equation admits a unique solution, thereby establishing probabilistic weak well-posedness. Our proof relies on the analysis of the associated Kolmogorov equations, which are Young-type parabolic PDEs with singular coefficients. The resulting theory for such singular Young-type parabolic PDEs is also of independent interest. |
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