Before revision:  In particular, for two high dimensional diffusion processes with the same integrated covariance matrix, the empirical spectral distributions of their RCVs can be very different. Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in generalnot a good proxy to rely on in the high dimensional caseenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.
After revision:  not a good proxy to rely on in the high dimensional caseenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.