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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 (Zn)n≥1 of the form Zn = Yn (mod 1)= {Yn}, where (Yn)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.

@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 = {}, }

Reference Type: Journal Article

Subject Area(s): Probability Theory