0/0}(z_s^{\mathbb P,t,\omega}-z_s^{\mathbb P,t,\omega'})\right|}^0+\int_{E}\scriptstyle e^{\alpha s}(u_s^{\mathbb P,t,\omega}-u_s^{\mathbb P,t,\omega'})^0(x)\nu^{t,\mathbb P}_s(dx)\right)ds\\ &\leq e^{\alpha T}{\left|\xi^{t,\omega}-\xi^{t,\omega'}\right|}^0+