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.
WEAK CONVERGENCE OF SEQUENCES FROM FRACTIONAL PARTS OF RANDOM VARIABLES AND APPLICATIONS
GIULIANO, RITA
2010-01-01
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.File in questo prodotto:
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