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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

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

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Received: 03.09.2003
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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
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\paper On almost sure behavior of stable subordinators over rapidly increasing sequences
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\pages 818--822
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\transl
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 4
\pages 718--722
\crossref{https://doi.org/10.1137/S0040585X97982128}
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