Asymptotic Behavior of Eigenvalues of Variance-Covariance Matrix of a High-Dimensional Heavy-Tailed Lévy Process

In this paper, we study the limiting behavior of eigenvalues of the variance-covariance matrix of a random sample from a multivariate subordinator heavy-tailed Lévy process, and use large deviations of a heavy-tailed stochastic process to derive the limit distributions of its components. We confine our study to multivariate Lévy processes with regularly varying random components and possibly different indices of regularity. Assuming that the …