On the rate of convergence to Rosenblatt-type distribution

TL;DR

This paper investigates how quickly certain stochastic processes converge to Rosenblatt-type distributions in non-central limit theorems, with detailed analysis for specific processes like Cauchy and Linnik's.

Contribution

It provides new results on the rate of convergence to Rosenblatt-type distributions using direct analytical methods, applicable to various processes and fields.

Findings

Established the rate of convergence in the uniform metric.

Analyzed convergence for Cauchy, Linnik's, and local-global distinguisher processes.

Discussed specific scenarios and conditions for convergence.

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.