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Rosenblatt distribution subordinated to Gaussian random fields with long-range dependence
| Content Provider | Scilit |
|---|---|
| Author | Leonenko, N. N. Ruiz-Medina, M. D. Taqqu, M. S. |
| Copyright Year | 2016 |
| Description | The Karhunen–Loève expansion and the Fredholm determinant formula are used to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of Gaussian stationary random fields on displaying long-range dependence. This distribution reduces to the usual Rosenblatt distribution when d = 1. Several properties of this new distribution are obtained. Specifically, its series representation, in terms of independent chi-squared random variables, is established. Its Lévy–Khintchine representation, and membership to the Thorin subclass of self-decomposable distributions are obtained as well. The existence and boundedness of its probability density then follow as a direct consequence. |
| Related Links | http://arxiv.org/pdf/1501.02247 |
| Ending Page | 177 |
| Page Count | 34 |
| Starting Page | 144 |
| ISSN | 07362994 |
| e-ISSN | 15329356 |
| DOI | 10.1080/07362994.2016.1230723 |
| Journal | Stochastic Analysis and Applications |
| Issue Number | 1 |
| Volume Number | 35 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2016-11-28 |
| Access Restriction | Open |
| Subject Keyword | Applied Mathematics Fredholm Determinant Hermite Polynomials Infinite Divisible Distributions Multiple Wiener–itô Stochastic Integrals Non-central Limit Theorems Rosenblatt-type Distribution |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability Statistics, Probability and Uncertainty |
