Estimates of the Rates of Convergence in Limit Theorems for the First Passage Times of Random Walks

Kennedy, Douglas P.

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 2090-2094 / Harvested from Project Euclid

Résumé

Let $T_r$ be the time of first passage to the level $r > 0$ by a random walk with independent and identically distributed steps and mean $\nu \geqq 0$. Estimates are given for the rate at which the distribution of $T_r$, suitably scaled and normalized, converges to the stable distribution with index $\frac{1}{2}$ when $\nu = 0$ and to the normal distribution when $\nu > 0$ as $r \rightarrow \infty$.

Publié le : 1972-12-14
Classification:

@article{1177690890,
     author = {Kennedy, Douglas P.},
     title = {Estimates of the Rates of Convergence in Limit Theorems for the First Passage Times of Random Walks},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 2090-2094},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177690890}
}

Kennedy, Douglas P. Estimates of the Rates of Convergence in Limit Theorems for the First Passage Times of Random Walks. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  2090-2094. http://gdmltest.u-ga.fr/item/1177690890/