On the LSL for Random Fields

Allan Gut () and Ulrich Stadtmüller ()
Additional contact information
Allan Gut: Uppsala University
Ulrich Stadtmüller: Ulm University

Journal of Theoretical Probability, 2011, vol. 24, issue 2, 422-449

Abstract: Abstract In some earlier work, we have considered extensions of Lai’s (Ann. Probab. 2:432–440, 1974) law of the single logarithm for delayed sums to a multi-index setting with the same as well as different expansion rates in the various dimensions. A further generalization concerns window sizes that are regularly varying with index 1 (on the line). In the present paper, we establish multi-index versions of the latter as well as for some mixtures of expansion rates. In order to keep things within reasonable size, we confine ourselves to some special cases for the index set $\mathbb{Z}_{+}^{2}$ .

Keywords: Delayed sums; Window; Law of the iterated logarithm; Law of the single logarithm; Sums of i.i.d. random variables; Slowly varying function; Multidimensional indices; Random fields; 60F15; 60G50; 60G60 (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-009-0265-z 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:24:y:2011:i:2:d:10.1007_s10959-009-0265-z

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

DOI: 10.1007/s10959-009-0265-z

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 ().