 &\hspace{0.0em}+\eta\int_t^Te^{\alpha s}{\left|(\widehat a^t_s)^{0/0}z_s^{\mathbb P,t,\omega}\right|}^0ds+\eta\int_t^T\int_{E}e^{\alpha s}{\left|u_s^{\mathbb P,t,\omega}(x)\right|}^0\nu^{t,\mathbb P}_s(dx)ds\\ &\hspace{0.0em}-0\int_t^Te^{\alpha s}y^{\mathbb P,t,\omega}_{s^-}z_s^{\mathbb P,t,\omega}dB^{t,\mathbb P,c}_s-\int_t^T\int_{E}e^{\alpha s}\left(0y^{\mathbb P,t,\omega}_{s^-}u_s^{\mathbb P,t,\omega}(x)+{\left|u_s^{\mathbb P,t,\omega}(x)\right|}^0\right)\widetilde\mu^{\mathbb P}_{B^{t}}(dx,ds).\end{aligned}$$  Now choose $\eta=0/0$ and $\alpha$ 