On the Distribution of the Maximum of the Sequence of Sums of Independent Random Variables

Gergley, T.; Yezhow, I. I.

Ann. Probab., Tome 3 (1975) no. 6, p. 289-297 / Harvested from Project Euclid

Résumé

Let $\xi_1, \xi_2, \cdots$ be independent random variables. The distribution of $\max (0, \xi_1, \xi_1 + \xi_2, \cdots, \xi_1 + \cdots + \xi_n)$ is investigated by means of a method based on the construction of certain events with easily determined proabilities. These yield a new formula for the distribution of the maximum which is sometimes more useful than that given in literature.

Publié le : 1975-04-14
Classification: Maximum distribution of, sums of independent random variables, random walk, 60G50, 60I15, 60F99

@article{1176996399,
     author = {Gergley, T. and Yezhow, I. I.},
     title = {On the Distribution of the Maximum of the Sequence of Sums of Independent Random Variables},
     journal = {Ann. Probab.},
     volume = {3},
     number = {6},
     year = {1975},
     pages = { 289-297},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996399}
}

Gergley, T.; Yezhow, I. I. On the Distribution of the Maximum of the Sequence of Sums of Independent Random Variables. Ann. Probab., Tome 3 (1975) no. 6, pp.  289-297. http://gdmltest.u-ga.fr/item/1176996399/