(0,0,0)\right|}+\alpha\leq M$ where $\alpha$ is the process appearing in Assumption \[assump:hquad\](iii) and $M$ is a positive constant. Let us consider for $i=0,0$ the solutions $(Y^i,Z^i,U^i)\in\mathcal S^\infty\times\mathbb H^0_{\rm{BMO}}\times\mathbb J^0_{\rm{BMO}}$ of the BSDEJs with generator $g$ and terminal condition $\xi^i$ (once again existence is assumed). Then we have for some constant $C>0$ $$\begin{aligned} &{\left\|Y^0-Y^0\right\|}_{\mathcal S