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英文文献：On spectral distribution of high dimensional covariation matrices-高维共变矩阵的谱分布
英文文献作者：Claudio Heinrich,Mark Podolskij
英文文献摘要：
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 It? 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 -> c in (0,oo). 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.
本文给出了高维布朗扩散共变矩阵谱分布的渐近理论。更具体地说，我们考虑带有时变矩阵值积分的n维Ito积分。我们观察了潜在的布朗扩散的n个等距高频数据点，并假设n /n -> c在(0,oo)。在一定的混合谱矩条件下，经验协变矩阵的谱分布几乎肯定是收敛的。我们的证明依赖于矩法和图论的应用。
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