  In this paper we present the asymptotic theory for spectral distributions of
high dimensional covariation matrices of Brownian diffusions. More
specifically, we consider $N$-dimensional Ito integrals with time varying
matrix-valued integrands. We observe $n$ equidistant high frequency data points
of the underlying Brownian diffusion and we assume that $N/n\rightarrow c\in
(0,\infty)$. We show that under a certain mixed spectral moment condition the
spectral distribution of the empirical covariation matrix converges in
distribution almost surely. Our proof relies on method of moments and
applications of graph theory.
