The Law of the Iterated Logarithm for Finitely Inhomogeneous Random Walks

Aurel Spătaru ()
Additional contact information
Aurel Spătaru: Romanian Academy

Journal of Theoretical Probability, 2010, vol. 23, issue 2, 417-427

Abstract: Abstract The Hartman–Wintner–Strassen law of the iterated logarithm states that if X 1, X 2,… are independent identically distributed random variables and S n =X 1+⋅⋅⋅+X n , then $$\limsup_{n}S_{n}/\sqrt{2n\log \log n}=1\quad \text{a.s.},\qquad \liminf_{n}S_{n}/\sqrt{2n\log \log n}=-1\quad \text{a.s.}$$ if and only if EX 1 2 =1 and EX 1=0. We extend this to the case where the X n are no longer identically distributed, but rather their distributions come from a finite set of distributions.

Keywords: Law of the iterated logarithm; Finitely inhomogeneous random walk; 60G50; 60F15 (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-009-0213-y 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:23:y:2010:i:2:d:10.1007_s10959-009-0213-y

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

DOI: 10.1007/s10959-009-0213-y

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 ().