On the rate of convergence to Rosenblatt-type distribution
arXiv:1412.6860 · doi:10.1016/j.jmaa.2014.12.016
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.
25 pages, 2 figures, typos corrected
References in corpus (5)
- Analysis of the Rosenblatt process
- Properties and numerical evaluation of the Rosenblatt distribution
- Limit theorems for weighted nonlinear transformations of Gaussian stationary processes with singular spectra
- Sojourn measures of Student and Fisher-Snedecor random fields
- Limit theorems for weighted functionals of cyclical long-range dependent random fields