Before revision:  A stable central limit theorem is attained with estimable asymptotic covariance matrix .
After revision:  A stable central limit theorem is attained with estimable asymptotic covariance matrices. This paper form a basis for infill asymptotic results of, for example, the realized Laplace transform, the realized principal component analysis, the continuous-time linear regression, and the generalized method of integrated moments, hence helps to extend the application scopes to more frequently sampled noisy data .