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December, 1981 A Functional Law of the Iterated Logarithm for a Class of Subordinators
R. P. Pakshirajan, R. Vasudeva
Ann. Probab. 9(6): 1012-1018 (December, 1981). DOI: 10.1214/aop/1176994271

Abstract

Let $\{X(t), t \in \lbrack 0, \infty)\}$ be a subordinator whose Levy spectral function $H(x)$ satisfies the inequality $c_1x^{-\alpha} \leq - H(x) \leq c_2x^{-\alpha},$ for all $x > 0$, for a $\alpha \in (0, 1)$ and for certain constants $c_1$ and $c_2, 0 < c_1 \leq c_2 < \infty$. In this paper we obtain (in the $M_1$ topology) the set of all almost sure limit functions of the sequence $(n^{-1/\alpha}X(nt))^{\frac{1}{\log \log n}}, t \in \lbrack 0, 1\rbrack, n \geq 3.$

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R. P. Pakshirajan. R. Vasudeva. "A Functional Law of the Iterated Logarithm for a Class of Subordinators." Ann. Probab. 9 (6) 1012 - 1018, December, 1981. https://doi.org/10.1214/aop/1176994271

Information

Published: December, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0477.60035
MathSciNet: MR632973
Digital Object Identifier: 10.1214/aop/1176994271

Subjects:
Primary: 60F15

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 6 • December, 1981
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