Sharp Conditions for the CLT of Linear Processes in a Hilbert Space

Florence Merlevède, Magda Peligrad and Sergey Utev

Journal of Theoretical Probability, 1997, vol. 10, issue 3, 681-693

Abstract: Abstract In this paper we study the behavior of sums of a linear process $$X_k = \sum {_{j = - \infty }^\infty } a_j (\xi _{k - j} )$$ associated to a strictly stationary sequence $$\{ \xi _k \} _{k \in \mathbb{Z}} $$ with values in a real separable Hilbert space and $$\{ a_k \} _{k \in \mathbb{Z}} $$ are linear operators from H to H. One of the results is that $$\sum {_{i = 1}^n } X_i /\sqrt n $$ satisfies the CLT provided $$\{ \xi _k \} _{k \in \mathbb{Z}} $$ are i.i.d. centered having finite second moments and $$\sum {_{j = - \infty }^\infty } \left\| {a_j } \right\|_{L(H)}

Keywords: Central limit theorem; linear process in Hilbert space (search for similar items in EconPapers)
Date: 1997
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/A:1022653728014 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:10:y:1997:i:3:d:10.1023_a:1022653728014

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1022653728014

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().