Holderian functional central limit theorem for linear processes
Let (Xt)t ≥ 1 be a linear process defined by Xt = ∑i=0∞ψi εt-1 where (ψi, i ≥ 0) is a sequence of real numbers and (εi , i ∈ Z) is a sequence of random variables with null expectation and variance 1. This paper provides Hölderian FCLT for (Xt)t ≥ 1 with wide class of filters. Filters with ψ(i)...
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Vilnius University Press
2004-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
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| Online Access: | https://www.journals.vu.lt/LMR/article/view/32281 |
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| author | Mindaugas Juodis |
| author_facet | Mindaugas Juodis |
| author_sort | Mindaugas Juodis |
| collection | DOAJ |
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Let (Xt)t ≥ 1 be a linear process defined by Xt = ∑i=0∞ψi εt-1 where (ψi, i ≥ 0) is a sequence of real numbers and (εi , i ∈ Z) is a sequence of random variables with null expectation and variance 1. This paper provides Hölderian FCLT for (Xt)t ≥ 1 with wide class of filters. Filters with ψ(i) = l(i)/i for a slowly varying function l(i) are allowed. The weak convergence of polygonal line process build from sums of (Xt)t ≥ 1 to the standard Brownian motion W in the Hölder space (Hα), 0 < α < 1/2 - 1/τ holds provided the proper noise behavior is satisfied: E|ε1|τ < ∞, τ > 2.
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| format | Article |
| id | doaj-art-41f5bd4ce86a43deb7dacaa656ae1370 |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2004-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-41f5bd4ce86a43deb7dacaa656ae13702025-01-20T18:16:15ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2004-12-0144spec.10.15388/LMR.2004.32281Holderian functional central limit theorem for linear processesMindaugas Juodis0Institute of Mathematics and Informatics Let (Xt)t ≥ 1 be a linear process defined by Xt = ∑i=0∞ψi εt-1 where (ψi, i ≥ 0) is a sequence of real numbers and (εi , i ∈ Z) is a sequence of random variables with null expectation and variance 1. This paper provides Hölderian FCLT for (Xt)t ≥ 1 with wide class of filters. Filters with ψ(i) = l(i)/i for a slowly varying function l(i) are allowed. The weak convergence of polygonal line process build from sums of (Xt)t ≥ 1 to the standard Brownian motion W in the Hölder space (Hα), 0 < α < 1/2 - 1/τ holds provided the proper noise behavior is satisfied: E|ε1|τ < ∞, τ > 2. https://www.journals.vu.lt/LMR/article/view/32281near convergencelinear processHolder space |
| spellingShingle | Mindaugas Juodis Holderian functional central limit theorem for linear processes Lietuvos Matematikos Rinkinys near convergence linear process Holder space |
| title | Holderian functional central limit theorem for linear processes |
| title_full | Holderian functional central limit theorem for linear processes |
| title_fullStr | Holderian functional central limit theorem for linear processes |
| title_full_unstemmed | Holderian functional central limit theorem for linear processes |
| title_short | Holderian functional central limit theorem for linear processes |
| title_sort | holderian functional central limit theorem for linear processes |
| topic | near convergence linear process Holder space |
| url | https://www.journals.vu.lt/LMR/article/view/32281 |
| work_keys_str_mv | AT mindaugasjuodis holderianfunctionalcentrallimittheoremforlinearprocesses |