  The estimation of the covariance structure from a discretely observed
multivariate Gaussian process under asynchronicity and noise is analysed under
high-frequency asymptotics. Asymptotic lower and upper bounds are established
for a general Gaussian framework which provides benchmark cases for various
Gaussian process models of interest. The parametric bounds give rise to
infinite-dimensional convolution theorems for covariation estimation under
asynchronicity, which is an essential estimation problem in finance.
