Control variates for dry friction under colored noise: variance rates for non-smooth observables

A control variate method was introduced by Garnier and Mertz (2022) for multivalued stochastic differential equations driven by colored noise. For smooth observables, the asymptotic variance is $O(\varepsilon^{2})$, where $\varepsilon^{2}$ is the correlation time of the noise. However, for non-smoot