Before revision:  Several examples of LPE , in which the conditions are shown to be satisfied assuming that the microstructure noise is O_p(1/\sqrt{n : estimation of volatility, powers of volatility, high-frequency covariance and volatility when incorporating trading information .
After revision:  Several examples of LPE are studied : estimation of volatility, powers of volatility, high-frequency covariance and volatility when incorporating trading information .