A Functional Law of the Iterated Logarithm for a Class of Subordinators

Pakshirajan, R. P.; Vasudeva, R.

Ann. Probab., Tome 9 (1981) no. 6, p. 1012-1018 / Harvested from Project Euclid

Résumé

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 $(n^{-1/\alpha}X(nt))^{\frac{1}{\log \log n}}, t \in \lbrack 0, 1\rbrack, n \geq 3.$

Publié le : 1981-12-14
Classification: Iterated logarithm, subordinators, stable subordinators, 60F15

@article{1176994271,
     author = {Pakshirajan, R. P. and Vasudeva, R.},
     title = {A Functional Law of the Iterated Logarithm for a Class of Subordinators},
     journal = {Ann. Probab.},
     volume = {9},
     number = {6},
     year = {1981},
     pages = { 1012-1018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994271}
}

Pakshirajan, R. P.; Vasudeva, R. A Functional Law of the Iterated Logarithm for a Class of Subordinators. Ann. Probab., Tome 9 (1981) no. 6, pp.  1012-1018. http://gdmltest.u-ga.fr/item/1176994271/