Before revision:  As an example of how to apply the limit theory provided in this paper, we build a time-varying friction parameter extension of the (semiparametric) model with uncertainty zones (Robert and Rosenbaum (2012)) and we show that we can verify the conditions for the estimation of integrated volatility.
After revision:  The framework is restricted to the (semiparametric) model with uncertainty zones (Robert and Rosenbaum (2012)) and we show that we can verify the conditions for the estimation of integrated volatility.