A Weak Convergence Theorem for Random Sums of Independent Random Variables
Fernandez, Pedro J.
Ann. Math. Statist., Tome 41 (1970) no. 6, p. 710-712 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
A limit theorem for random sums of independent random elements of $D\lbrack 0, 1\rbrack$ is proved. The theorem extends and simplifies the proof of a result obtained by R. Pyke in [3]. In a personal communication Professor Pyke remarked to me that the method employed is also the right approach to the problem studied in [4], by adequately defining sequences of random elements of $D\lbrack 0, 1 \rbrack$.
Publié le : 1970-04-14
Classification:  
@article{1177697120,
     author = {Fernandez, Pedro J.},
     title = {A Weak Convergence Theorem for Random Sums of Independent Random Variables},
     journal = {Ann. Math. Statist.},
     volume = {41},
     number = {6},
     year = {1970},
     pages = { 710-712},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177697120}
}

Fernandez, Pedro J. A Weak Convergence Theorem for Random Sums of Independent Random Variables. Ann. Math. Statist., Tome 41 (1970) no. 6, pp.  710-712. http://gdmltest.u-ga.fr/item/1177697120/