In this paper, we study the existence of densities (with respect to the Lebesgue measure) for marginal laws of the solution $(Y,Z)$ to a quadratic growth BSDE. Using the (by now) well-established connection between these equations and their associated semi-linear PDEs, together with the Nourdin–Viens formula, we provide estimates on these densities.
"Density analysis of BSDEs." Ann. Probab. 44 (4) 2817 - 2857, July 2016. https://doi.org/10.1214/15-AOP1035