### Giuliano, R (2011)

#### Weak convergence of sequences from fractional parts of random variables and applications

Theory of Probability and Mathematical Statistics 83, pp. 59-69.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1090/S0094-9000-2012-00841-7

**Abstract:** We prove results concerning the weak convergence to the uniform distribution on [0, 1] of sequences (Z_{n})_{n≥1} of the form Z_{n} = Y_{n} (mod 1)= {Y_{n}}, where (Y_{n})_{n≥1} is a general sequence of real random variables. Applications are given: (i) to the case of partial sums of (i.i.d.) random variables having a distribution belonging to the domain of attraction of a stable law; (ii) to the case of sample maxima of i.i.d random variables.

**Bibtex:**

```
@article{,
AUTHOR = {Rita Giuliano},
YEAR = {2011},
JOURNAL = {Theor. Probability and Math. Statist.},
VOLUME = {83},
PAGES = {59--69},
DOI = {10.1090/S0094-9000-2012-00841-7 },
URL = {http://www.ams.org/journals/tpms/2011-83-00/S0094-9000-2012-00841-7/S0094-9000-2012-00841-7.pdf},
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Probability Theory