This paper surveys some recent developments in non-central limit theorems for long-range dependent random processes and fields. We describe an increasing domain framework for asymptotic behavior of functionals of random processes and fields. Recent results on the rate of convergence to the Hermite-type distributions in non-central limit theorems are presented. The use of these results is demonstrated through an application to the case of Rosenblatt-type distributions.
Funding
The first author was supported in part under the Australian Research Council’s Discovery Projects funding scheme (project number DP160101366). The second author was supported in part under the Australian Research Council’s Discovery Projects funding scheme (project number DP160101366) and by the La Trobe University DRP Grant in Mathematical and Computing Sciences.
Publication Date
2017-01-01Journal
Theory of Probability and Mathematical StatisticsVolume
95Pagination
13p. (p. 3-15)Publisher
American Mathematical SocietyISSN
0094-9000Rights Statement
First published in Theor. Probability and Math. Statist. 95 (2017), published by the American Mathematical Society. © 2018 American Mathematical Society.
This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
