Before revision:  We then show that if the perturbation corresponds to\operatorname{rd} }\to rounding to the nearest point in some fixed discrete set , the bounds on the difference of moments can be improved to quadratic in many cases.
After revision:  We then show that if the perturbation corresponds to\operatorname{rd} : \mathbb{R}\to rounding to the nearest point in some fixed discrete set , the bounds on the difference of moments can be improved to quadratic in many cases.