  We develop an asymptotic theory for the jump robust measurement of
covariations in the context of stochastic evolution equation in infinite
dimensions. Namely, we identify scaling limits for realized covariations of
solution processes with the quadratic covariation of the latent random process
that drives the evolution equation which is assumed to be a Hilbert
space-valued semimartingale. We discuss applications to dynamically consistent
and outlier-robust dimension reduction in the spirit of functional principal
components and the estimation of infinite-dimensional stochastic volatility
models.
