 &\hspace{0.0em}+\eta\int_t^Te^{\alpha s}{\left|(\widehat a^t_s)^{0/0}(z_s^{\mathbb P,t,\omega}-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)-u_s^{\mathbb P,t,\omega'}(x)\right|}^0\nu^{t,\mathbb P}_s(dx)ds\\ &\hspace{0.0em}