Asymptotics of Randomly Stopped Sequences with Independent Increments

Greenwood, Priscilla

Ann. Probab., Tome 1 (1973) no. 5, p. 317-321 / Harvested from Project Euclid

Résumé

Let $S_n, n = 1, 2, \cdots$, be a sequence of sums of independent, identically distributed random variables $X_i$ such that $P\{X_i > y\}$ is a regularly varying function of $y$ at infinity. Let $N$ be a stopping time for $S_n$ with finite mean. A necessary and sufficient condition is given that $$\lim_{y\rightarrow \infty} P\{S_N > y\}/P\{X_1 > y\} = EN.$$ Examples further illustrate the role of this condition.

Publié le : 1973-04-14
Classification: Stopping times, random sums, regular variation, independent increments, asymptotics, 60G40, 60G50

@article{1176996984,
     author = {Greenwood, Priscilla},
     title = {Asymptotics of Randomly Stopped Sequences with Independent Increments},
     journal = {Ann. Probab.},
     volume = {1},
     number = {5},
     year = {1973},
     pages = { 317-321},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996984}
}

Greenwood, Priscilla. Asymptotics of Randomly Stopped Sequences with Independent Increments. Ann. Probab., Tome 1 (1973) no. 5, pp.  317-321. http://gdmltest.u-ga.fr/item/1176996984/