On the rate of convergence to Rosenblatt-type distribution

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.