On rate of convergence in non-central limit theorems

The case when the summands/integrands are functionals of a long-range dependent Gaussian process is of great importance in the theory of limit theorems for sums/integrals of dependent random variables. Comparing with the CLT, long-range dependent summands can produce different normalizing coefficients and non-Gaussian limits. Integral functionals of homogeneous random fields/processes with long-range dependence are investigated.  The main result is the rate of convergence to the Hermite-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. 

The presentation is based on the manuscript:
Vo Anh, N. Leonenko, A.Olenko, V.Vaskovych. On rate of convergence in non-central limit theorems, submitted.