The limit points in $\bar{R^d}$ of averages of i.i.d. random variables
Erickson, K. Bruce
Ann. Probab., Tome 28 (2000) no. 1, p. 498-510 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Given any closed subset $C$ of $\bar{R^d}$, containing a pair of antipodal points at $\infty$, there is a sequence of independent and identically distributed random variables $\mathbf{X}_i}$ such that the set of limit points (in the topology of $\bar{R^d}$ of $\{(\mathbf{X}_1 + \cdots + \mathbf{X}_t)/t\}_{t \geq 1}$ equals $C$. Here $\bar{R^d}$ is the compact space gotten by “adjoining the sphere, $S^{d -1}\infty$ at infinity.”
Publié le : 2000-01-14
Classification:  Normalized random walk,  limit points,  60F05,  60F15 
@article{1019160128,
     author = {Erickson, K. Bruce},
     title = {The limit points in $\bar{R^d}$ of averages of i.i.d. random
		 variables},
     journal = {Ann. Probab.},
     volume = {28},
     number = {1},
     year = {2000},
     pages = { 498-510},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1019160128}
}

Erickson, K. Bruce. The limit points in $\bar{R^d}$ of averages of i.i.d. random
		 variables. Ann. Probab., Tome 28 (2000) no. 1, pp.  498-510. http://gdmltest.u-ga.fr/item/1019160128/