Rate of convergence to the Rosenblatt distribution for additive functionals of stochastic processes with long-range dependence (Q5943715)

The paper is concerned with the important and difficult problem of sharp convergence rate in non-central limit theorems. The authors provide the rate of convergence (in the uniform Kolmogorov distance) of probability distributions of normalized integral functionals of Gaussian processes with long-range dependence to a limiting non-Gaussian distribution called the Rosenblatt distribution. For technical reasons, they use the covariance function \(B(t)\) of the Gaussian processes of the form \(B(t)= 1/(1+ t^2)^{\alpha/2}\), \(0< \alpha< 1\), \(-\infty< t<\infty\).