Strassen-type laws for independent random walks

Karl Grill

Stochastic Processes and their Applications, 1997, vol. 71, issue 1, 1-10

Abstract: Let (Xij) be a double sequence of independent, identically distributed random variables, with mean zero and variance one, whose moment generating function is finite in a neighbourhood of the origin. Let Si(t) be the partial sum process constructed from Xi. We consider the sets Fn = {[gamma]-1nSi(n.):i [less-than-or-equals, slant] an}, where an is a nondecreasing sequence of integers and [gamma]n is a suitable normalizing sequence. We prove a strong approximation result that in particular implies a Strassen-type law if an grows slower than exponential. If an grows at an exponential rate, we prove another Strassen-type result.

Keywords: Functional; laws; Strong; approximation; Sums; of; independent; random; variables (search for similar items in EconPapers)
Date: 1997
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00043-4
Full text for ScienceDirect subscribers only

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:eee:spapps:v:71:y:1997:i:1:p:1-10

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().