On the rate of convergence to Rosenblatt-type distribution

Abstract

The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid to the Cauchy, generalized Linnik's, and local-global distinguisher random processes and fields. Direct analytical methods are used to investigate the rate of convergence in the uniform metric.