In this paper we obtain the scaling limit of multidimensional Levy walk and describe the detailed structure of the limiting process. It occurs that the scaling limit is a subordinated alpha-stable Levy motion with the parent process and subordinator being strongly dependent processes. The...

Given a reference random variable, we study the solution of its Stein equation and obtain universal bounds on its first and second derivatives. We then extend the analysis of Nourdin and Peccati by bounding the Fortet–Mourier and Wasserstein distances from more general random variables such as...

Scatter plots for two multivariate normal data sets may suggest that the constant-density ellipsoid contours of underlying density functions have the same directions. In other words, covariance matrices of the two populations have the same eigenvectors matrix in their spectral decomposition...

This paper precisely characterizes asymptotic behaviors of the volatilities in nonstationary GARCH(1, 1) models. After suitable renormalization, it is shown that the volatility converges in distribution to a non-degenerate limit. This provides more insight into the dynamics of volatilities in...