RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 4, Pages 818–822 (Mi tvp138)

Short Communications

On almost sure behavior of stable subordinators over rapidly increasing sequences

R. Vasudevaa, G. Divanjibc

a Department of Statistics, University of Mysore
b Department of Statistics, Sri Krishnadevaraya University
c Department of Statistics, University of Botswana

Abstract: Let $(X(t), t\geq 0)$ with $X(0)=0$ be a stable subordinator with index $0<\alpha<1$ and let $(t_k)$ be an increasing sequence such that $t_{k+1}/t_k\to\infty$ as $k\to\infty$. Let $(a_t)$ be a positive nondecreasing function of $t$ such that $a(t)/t\leq 1$. Define $Y(t)=X(t+a(t))-X(t)$ and $Z(t)=X(t)-X(t-a(t))$, $t>0$. We obtain law-of-the-iterated-logarithm results for $(X(t_k)),(Y(t_k))$ and $Z(t_k)$, properly normalized.

Keywords: law of iterated logarithm, subsequences, stable subordinators, almost sure bounds.

DOI: https://doi.org/10.4213/tvp138

Full text: PDF file (536 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2006, 50:4, 718–722

Bibliographic databases:

Language:

Citation: R. Vasudeva, G. Divanji, “On almost sure behavior of stable subordinators over rapidly increasing sequences”, Teor. Veroyatnost. i Primenen., 50:4 (2005), 818–822; Theory Probab. Appl., 50:4 (2006), 718–722

Citation in format AMSBIB
\Bibitem{VasDiv05} \by R.~Vasudeva, G.~Divanji \paper On almost sure behavior of stable subordinators over rapidly increasing sequences \jour Teor. Veroyatnost. i Primenen. \yr 2005 \vol 50 \issue 4 \pages 818--822 \mathnet{http://mi.mathnet.ru/tvp138} \crossref{https://doi.org/10.4213/tvp138} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2331995} \zmath{https://zbmath.org/?q=an:1117.60016} \elib{http://elibrary.ru/item.asp?id=9157521} \transl \jour Theory Probab. Appl. \yr 2006 \vol 50 \issue 4 \pages 718--722 \crossref{https://doi.org/10.1137/S0040585X97982128} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000243284300016}